Lesson #5- Geometric Probability

Geometric Probability There are 3 types of geometric probabilities, one for each of the commonly used dimensions of space; length, area and volume. Target length 1D P(Target) = Total length Target area 2D P(Target) = Total area Target volume 3D P(Target) = Total volume

There is an 18% chance the blind mouse will escape into the hole. Eg. 1 What is the probability that the blind mouse will escape into a hole? Target length P(Target) = 90 cm Total length 16 cm = 90 cm 8 = 45 8 cm Probability of Volume = 0.18 There is an 18% chance the blind mouse will escape into the hole.

Target A Target B Target C The dart will hit Target C Eg. 2 Which black target is a skydiver most likely to land on? Target A Target B Target C 6 m 4 m 6 m 6 m = Asquare P(B) = ABcircle -AScircle Pr2 - Pr2 s2 P(3)2 – P(2)2 62 9P – 4P 36 5P = 0.436 = P(A) = Target area Total area 4 black squares 9 total squares 4 9 0.444 P(C) = Target area Total area = 4(b)(h))/ 2 s2 2(3)(3) 62 18 36 0.5 The dart will hit Target C

Vcone Vprism Target volume Total volume Eg. 3 What is the probability the bee is in the laser cone? Vcone h=6 m Vprism s = 8 m Target volume P(Cone) = Total volume The probability the bee is in the cone is 26%

Geometric Probability Worksheet Homework Geometric Probability Worksheet