Question

The letters P-R-O-B-A-B-I-L-I-T-Y are written on a set of cards. You mix the cards thoroughly. Without looking, you draw one letter then you draw another without replacing the first. Find the probability that you will select a P followed by a Y.

P(P, then Y) =

Answer 1

P(P, then Y)=(1/11)(1/10)=1/110

Explanation:

The number of letters in probability is 11.

There is 1 P.

The probability of drawing a P on draw 1 is the number of ways of drawing a P, which is 1, divided by the number of ways of drawing any letter, which is 11. Thus:

Probability of drawing a P on the first draw is 1/11.

There are now 10 letters left. There is 1 Y. so

Probability of drawing a Y on the second draw given that you drew a P on the first draw is 1/10.

The probability of drawing a P on the first draw and a Y on the second draw is

(probability of a P on draw 1)(probability of drawing a Y on draw 2, given a P on draw 1)

P(P, then Y)=(1/11)(1/10)=1/110