Question

A card is drawn from a well-shuffled deck of 52 cards and without replacing this card, a second card is drawn. Find the probability that the first card is a club and the second card is a spade.

Answer 1

Given: a well shuffled deck of 52 cards. Each draw is independent of the other.

To find: the probability that the first card is drawn is a club and the second card is a spade.

Let , success for the first trail be getting a club.

Now , the Probability of success in the first trial is

P₁(success) = \(\frac{13}{52}\)

let , success for the second trail be getting a spade.

Probability of success in the second trial without replacement of the first draw is given by

P₂(success) = \(\frac{13}{51}\)

Hence , the probability that the first card is drawn is a club and the second card is a spade ,with each trial being independent is given by