Question

The probability that a student pilot passes the written test for a private pilot's license is 0.7. what is the probability that the student will pass the test on the third try? before the fourth try?

Answer 1

Probability = 0.063 Fourth try = 0.0973 Let X be the number of failed attempts at passing the test before the student passes. This is a negative binomial or geometric variable with x â {0, 1, 2, 3, . . .}, p = P(success) = 0.7 and the number of successes to to observe r = 1. Thus the pmf is nb(x; 1, p) = (1 â’ p) xp. The probability P that the student passes on the third try means that there were x = 2 failed attempts or P = nb(2, ; 1, .7) = (.3)2 (.7) = 0.063 . The probability that the student passes before the third try is that there were two or fewer failed attmpts, so P = P(X ≤ 2) = nb(0, ; 1, .7) + nb(1, ; 1, .7) + nb(2, ; 1, .7) = (.3)0 (.7) + (.3)1 (.7) + (.3)2 (.7) = 0.973 .