Question

A locker combination consists of two non-zero digits. the digits in a combination are not repeated and range from 2 through 9. event a = the first digit is less than 5 event b = the second digit is less than 5 if a combination is picked at random, with each possible locker combination being equally likely, what is p(b|a) expressed in simplest form?

Answer 1

1/3.

Explanation:

P(event a occurs) = 3/9 = 1/3

P(event b occurs) = 3/9 = 1/3

P(a) ∩ P(b) = 1/3 * 1/3 = 1/9

P(b|a) = P(a) ∩ P(b) / P(a)

= 1/9 / 1/3

= 1/3.