Question

John often speed while driving to school in order to arrive on time. The probability that he will speed to school is 0.75. If the probability that he speeds and gets stopped by a police officer is 0.25. Find the probability that he is stopped, given that he is speeding.

Answer 1

0.33

Explanation:

Given the following :

P(speeding) = p(s) = 0.75

P(being stopped) = p(t)

P(speeding and gets stopped) = p(s n t) = 0.25

Find the probability that he is stopped, given that he is speeding is written as P(t | s) ;

P(t | s) = p(s n t) / p(s)

P(s n t) = 0.25

P(s) = 0.75

Hence,

P(t | s) = 0.25 / 0.75

P(t | s) = 0.33