Letter tiles that spell the words HAPPINESS are placed in a bag. A tile is drawn and replaced and then a second tile is drawn. Find p(vowel,then p).
There are 3 vowels in the word HAPPINESS (A, E, and I) and 8 total letters.
So the probability of drawing a vowel on the first draw is 3/8.
Since the tile is replaced, the probability of drawing a P on the second draw is also 1/8.
So the probability of drawing a vowel on the first draw and a P on the second draw is:
(3/8) x (1/8) = 3/64
Therefore, p(vowel, then P) = 3/64.