Question

If cards are drawn one by one from a well shuffled pack of 52 cards without replacement, until an ace appears, find the probability that the fourth card is the first ace to appear.

Answer 1

Probability of selecting 3 non-Ace and 1 Ace out of 52 cards is equal to

Since we want 4th card to be first ace, we will also have to consider the arrangement, Now 4 cards in sample space can be arranged in 4! ways and, favorable they can be arranged in 3! ways as we want 4th position to be occupied by ace

Hence required probability