{"id":447,"date":"2022-04-13T11:01:09","date_gmt":"2022-04-13T11:01:09","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=447"},"modified":"2024-11-16T05:36:44","modified_gmt":"2024-11-16T05:36:44","slug":"x-5-probability-of-independent-and-dependent-events","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/x-5-probability-of-independent-and-dependent-events\/","title":{"rendered":"X.5 Probability of independent and dependent events"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Probability of independent and dependent events<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-f79afd6ea8b322268468366b8e5f7cc7\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-439b87561eb4d58e0018c04df6f8b770\" style=\"color:#000060\">1. <strong>Probability Overview<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Probability is a measure of the likelihood or chance that a specific event will occur. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.<\/li>\n\n\n\n<li>Probability ranges from 0 (impossible event) to 1 (certain event).<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-c469d382effe89cbdebfd89a4ec6b260\" style=\"color:#000060\">2. <strong>Independent Events<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Definition<\/strong>: Two events are independent if the occurrence of one event does not affect the occurrence of the other event.<\/li>\n\n\n\n<li><strong>Example<\/strong>: Tossing a coin and rolling a die. The result of the coin toss does not affect the die roll.<\/li>\n\n\n\n<li><strong>Probability of Independent Events<\/strong>:<\/li>\n\n\n\n<li>If A and B are independent events, the probability of both A and B occurring is:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">P(A\u00a0and\u00a0B)=P(A)\u00d7P(B)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For example, the probability of tossing a head (P(A) = 1\/2) and rolling a 3 on a die (P(B) = 1\/6) is:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"67\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-55.png\" alt=\"\" class=\"wp-image-14609\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-55.png 344w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-55-300x58.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/figure><\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-01381f816d6309efe383ed150e5fd9bc\" style=\"color:#000060\">3. <strong>Dependent Events<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Definition<\/strong>: Two events are dependent if the occurrence of one event affects the occurrence of the other event.<\/li>\n\n\n\n<li><strong>Example<\/strong>: Drawing cards from a deck without replacement. The first draw affects the probability of the second draw.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9dfe359a5641bf631a9461669809d175\" style=\"color:#000060\"><strong>Probability of Dependent Events<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If A and B are dependent events, the probability of both A and B occurring is: P(A&nbsp;and&nbsp;B)=P(A)\u00d7P(B\u2223A)<\/li>\n\n\n\n<li>where P(B\u2223A)P(B|A)P(B\u2223A) is the conditional probability of B occurring given that A has occurred.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For example, if you draw a card from a deck and it is a heart (P(A) = 13\/52), the probability of drawing another heart on the second draw (without replacement) would be:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"301\" height=\"65\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/11\/image-53.png\" alt=\"\" class=\"wp-image-14605\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example <\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color wp-elements-d9b9b1ed26c985e6c71d27d0c450f0a8\" style=\"background-color:#fcc2c6\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-89559bf529035fea1bd96cdf2da88511\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>You spin the spinner twice.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-12-1.png\" alt=\"\" class=\"wp-image-11034\" style=\"width:220px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-12-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-12-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-12-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-8bd355d31ed4dbce293057afe9f0901e\" style=\"color:#b00012\"><strong>What is the probability of landing on an even number and then landing on a 5?<\/strong><\/p>\n\n\n\n<p><em>Write your answer as a percentage.<\/em><\/p>\n\n\n\n<p>______ %<\/p>\n<\/div><\/div>\n\n\n\n<p>The events&nbsp;<strong>even<\/strong>&nbsp;and&nbsp;<strong>5<\/strong>&nbsp;are independent. The first spin does not affect the second spin.<\/p>\n\n\n\n<p>Find P(even). The spinner has 4 equal sections, numbered 4, 5, 6 and 7. The even numbers are 4 and 6. There are 2 even numbers.<\/p>\n\n\n\n<p>P(even) = 2\/4<\/p>\n\n\n\n<p>Find P(5).<\/p>\n\n\n\n<p>P(5) = 1\/4.<\/p>\n\n\n\n<p>Find the probability of landing on an even number and then landing on a 5. Multiply P(even) by P(5).<\/p>\n\n\n\n<p>P(even) x P(5) = 2\/4 x 1\/4 .<\/p>\n\n\n\n<p>= 2\/16 .<\/p>\n\n\n\n<p>Write your answer as a decimal. Then convert your answer to a percentage.<\/p>\n\n\n\n<p>2\/16 = 0.125 = 12.5%<\/p>\n\n\n\n<p>The probability of landing on an even number and then landing on a 5 is 12.5%.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color wp-elements-324cd251feb1836f7a3de5b51feb1a35\" style=\"background-color:#f7c0f8\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-090a9c4d4b2ac3772cd8321a78cefc89\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>You roll a 6-sided die two times.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-13-1.png\" alt=\"\" class=\"wp-image-11037\" style=\"width:220px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-13-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-13-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-13-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-47fda9bd13d842f9b25c08517de85af6\" style=\"color:#b00012\"><strong>What is the probability of rolling a number less than 5 and then rolling a number greater than 5?<\/strong><\/p>\n\n\n\n<p><em>Simplify your answer and write it as a fraction or whole number.<\/em><\/p>\n<\/div><\/div>\n\n\n\n<p>The events&nbsp;<strong>less than 5<\/strong>&nbsp;and&nbsp;<strong>greater than 5<\/strong>&nbsp;are independent. The first roll does not affect the second roll.<\/p>\n\n\n\n<p>Find P(less than 5). The die has 6 sides, numbered 1, 2, 3, 4, 5 and 6. The numbers less than 5 are 1, 2, 3 and 4. There are 4 numbers less than 5.<\/p>\n\n\n\n<p>P(less than 5) = 4\/6 .<\/p>\n\n\n\n<p>Find P(greater than 5). The only number greater than 5 is 6. There is 1 number greater than 5.<\/p>\n\n\n\n<p>P(greater than 5) = 1\/6 .<\/p>\n\n\n\n<p>Find the probability of rolling a number less than 5 and then rolling a number greater than 5. Multiply P(less than 5) by P(greater than 5).<\/p>\n\n\n\n<p>P(less than 5) x P(greater than 5) = 4\/6 x 1\/6 .<\/p>\n\n\n\n<p>= 4\/36 .<\/p>\n\n\n\n<p>Write your answer in simplest form.<\/p>\n\n\n\n<p>4\/36 = 1\/9 .<\/p>\n\n\n\n<p>The probability of rolling a number less than 5 and then rolling a number greater than 5 is 1\/9.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-c7ed35c90d0e7c988d258c628978ec2d\" style=\"background-color:#c8f7ca\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-1be3db53adf648d651a3eee08daa69db\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>You pick a card at random. Without putting the first card back, you pick a second card at random.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-14-1.png\" alt=\"\" class=\"wp-image-11047\" style=\"width:385px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-14-1.png 670w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/Untitled-design-14-1-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-ae7d6e2ec13ff8d90f8a5f9b9e4d477b\" style=\"color:#b00012\"><strong>What is the probability of picking a prime number and then picking a prime number?<\/strong><\/p>\n\n\n\n<p><em>Write your answer as a percentage.<\/em><\/p>\n\n\n\n<p>_______ %<\/p>\n<\/div><\/div>\n\n\n\n<p>Find P(prime). There are 4 cards, numbered 6, 7, 8 and 9. The only prime number is 7.<\/p>\n\n\n\n<p>P(prime) = 1\/4 .<\/p>\n\n\n\n<p>Now find the probability of picking a prime number once you have already picked a prime number.<\/p>\n\n\n\n<p>There are 3 cards remaining. None of those cards is a prime number.<\/p>\n\n\n\n<p>After you have picked a prime number, the probability of picking a prime number is 0.<\/p>\n\n\n\n<p>Find the probability of picking a prime number and then picking a prime number. Multiply P(prime) by P(prime).<\/p>\n\n\n\n<p>P(prime) x P(prime) = 1\/4 \/ 0\/3<\/p>\n\n\n\n<p>= 0\/12<\/p>\n\n\n\n<p>Write your answer as a decimal. Then convert your answer to a percentage.<\/p>\n\n\n\n<p>0 = 0 = 0%<\/p>\n\n\n\n<p>The probability of picking a prime number and then picking a prime number is 0%.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/75552\/970\/949\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-163.png\" alt=\"\" class=\"wp-image-7493\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-163.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-163-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-163-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/80935\/319\/959\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-182.png\" alt=\"\" class=\"wp-image-7494\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-182.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-182-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-182-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Probability of independent and dependent events Key Notes: 1. Probability Overview 2. Independent Events P(A\u00a0and\u00a0B)=P(A)\u00d7P(B) 3. Dependent Events Probability of Dependent Events: Learn with an example You spin the spinner twice. What is the probability of landing on an even number and then landing on a 5? Write your answer as a percentage. ______ %<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/x-5-probability-of-independent-and-dependent-events\/\">Continue reading <span class=\"screen-reader-text\">&#8220;X.5 Probability of independent and dependent events&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-447","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/447","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=447"}],"version-history":[{"count":20,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/447\/revisions"}],"predecessor-version":[{"id":14611,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/447\/revisions\/14611"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}