Question

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.

Answer 1

Answer:

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:

$P(H)=\frac{13}{52}=0.25$

Compute the probability of selecting a Spade second as follows:

$P(S)=\frac{13}{51}=0.255$

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:

$P(1st\ H\cap 2nd\ S)=P(H)\times P(S)$

                            $=0.25\times 0.255\\=0.06375\\\approx 0.064$

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