Geometry 11.7 Big Idea: Find Geometric Probability

Vocabulary: Probability of an event: the likelihood that an event will occur The probability is always between 0 and 1 and can be expressed as a fraction, decimal or percent.

Ex. If you randomly pull a marble from a bag of 12 blue marbles and 8 white marbles, the probability of pulling a white marble is Probability = # of favorable outcomes # of total possible outcomes = # of white marbles # of total marbles

Vocabulary: Geometric probability: A ratio that involves a geometric ratio such as length or area and the probability that a point P will be found randomly in that location

Probability and Length If a point K is picked randomly on line segment PQ, the probability it is on line segment PR is ratio of length PR/PQ. P(K) = PR P(K) = PR PQ PQ

Example: Find the probability that a point chosen at random on PQ is on RS.

Example: Find the probability that a point chosen at random on PQ is on the given segment.

Probability and Area If a point K is picked randomly from region R, which includes region S, the probability it is in region S is the ratio of area S to ratio of area R. P(K) = Area of S P(K) = Area of S Area of R Area of R

Example: The diameter of the dartboard is 80 cm. The diameter of the red bulls eye is 16 cm. If an arrow is shot at the dartboard, find the probability of hitting the bulls eye.

Example: Find the probability that a randomly chosen point lies in the shaded region.