Let X be the sum of the two bills selected. Then P(X>16)?

Question

A box contains one $5 bill, three $10 bills, and four $20 bilis. A bill is selected at random, and it is not replaced: then a second bill is selected at random. Let X be the sum of the two bills selected.

Answer 1

The box contains 8 bills total, so picking two without replacement gives 8·7 = 56 distinct outcomes in the sample space, all of equal probability.

Of those 56 outcomes, the only outcomes that yield a sum ≤ 16 are picking a $5 bill 1st and a $10 bill 2nd or a $10 bill 1st and a $5 bill 2nd: 1/8·4/7 + 4/8·1/7 = 8/56.

P(X > 16) = 1 - 8/56 = 48/56