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?

A. 1/4
B. 2/7
C. 4/9
D. 1/2

Answer choice B

Step-by-step explanation:

There are two possibilities; in the first, the first digit is below 5, in the second, it is above. The probability of the first possibility is 3/8, because there are 3 possible digits below 5 and 8 total digits. In this scenario, the chance of the second digit being below 5 is 2/7, because one of the digits is taken. In the other possibility, which has a chance of 5/8, the probability of choosing a number below 5 is 3/7, since all of them are still available. Doing the arithmetic, you find that the total probability is 2/7. Hope this helps!

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