Geometric probability

Key Notes:

🎯 Probability is the measure of how likely an event is to occur.If a line segment is completely contained in another and a point on the larger segment is chosen at random, the probability it is also on the smaller segment equals the length of the smaller segment divided by the length of the larger segment.

If a point E on AD is chosen at random, the probability that E is on BC is BC/AD

Learn with an example

🏫 A point on the line segment is chosen at random. What is the probability it is between 57 and 58?

Simplify your answer and write it as a proper fraction._______

  • Look at the line segment.46,48,50,52,54,56,58
  • The segment between 57 and 58 is completely contained in the total segment. The length of the shorter segment is the absolute value of the difference between its left endpoint and right endpoint, which is |57–58|=1.
  • Similarly, the total length of the segment is |46–58|=12.
  • Divide the lengths to find the probability that a randomly chosen point between 46 and 58 is also between 57 and 58.The probability is 1/12.

🏫 A point on the line segment is chosen at random. What is the probability it is between 49 and 50?45,46,47,48,49,50,51

🏫 ,Simplify your answer and write it as a proper fraction._____

  • Look at the line segment.45,46,47,48,49,50,51
  • The segment between 49 and 50 is completely contained in the total segment. The length of the shorter segment is the absolute value of the difference between its left endpoint and right endpoint, which is |49–50|=1.
  • Similarly, the total length of the segment is |45–51|=6
  • Divide the lengths to find the probability that a randomly chosen point between 45 and 51 is also between 49 and 50.The probability is 1/6.

🏫 A point on the line segment is chosen at random. What is the probability it is between 57 and 63?

🏫 Simplify your answer and write it as a proper fraction._______

  • Look at the line segment.
  • The segment between 57 and 63 is completely contained in the total segment. The length of the shorter segment is the absolute value of the difference between its left endpoint and right endpoint, which is |57–63|=6.
  • Similarly, the total length of the segment is |56–63|=7.
  • Divide the lengths to find the probability that a randomly chosen point between 56 and 63 is also between 57 and 63.The probability is 6/7.

Let’s practice!🖊️