Down the Road G2

Conditional Probability

Kelvin and Cynthia are getting their G2. Kelvin is the first to take the test and Cynthia takes it next. According to PassTheWheel.com, the pass rate is 64%. The probability of Kelvin and Cynthia passing is 70%. Kelvin failed on his first attempt. Cynthia is nervous for her driver’s test and she calculates the probability of her failing given that Kelvin failed.

Answer: This is a conditional probability problem because the probability of Cynthia failing her G2 (B) is created based on the probability of Kelvin failing his G2 (A). Therefore, the probability of B is dependent of the probability of A.
 

A = Kelvin failing G2                        

B = Cynthia failing G2

P(A∩B) = 1-0.7 = 0.3

P(A) = 1.0.64 = 0.36

P(B|A) = P(A∩B)

                 P(A)

            = 0.3

               0.36

            = 0.83333/ 83.33%

∴ the probability Cynthia failing the test is 83.33% given that Kelvin failed the first time.