You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a Heart and the second card is a Spade. Write your answer as a decimal rounded to four places if necessary.

The probability that the first card is a Heart and the second card is a Spade is 0.064.

Step-by-step explanation:

A standard deck of 52 cards is shuffled and two cards are drawn without replacement.

The denominations of the cards are as follows:

Spades (S) = 13

Hearts (H) = 13

Diamonds (D) = 13

Clubs (C) = 13

Compute the probability of selecting a Heart first as follows:

Compute the probability of selecting a Spade second as follows:

Since the two cards are selected without replacement the second draw is independent of the other.

Then the probability that the first card is a Heart and the second card is a Spade is:

Thus, the probability that the first card is a Heart and the second card is a Spade is 0.064.

853.3

step-by-step explanation: