Question

There are 52 cards in a standard deck: 13 hearts, 13 clubs, 13 diamonds , and 13 spades. Timothy draws four cards at random from the deck, one of each suit. If he draws again , without replacing the four he drew, what is the probability that the next card is a heart

Answer 1

Answer:

$\dfrac{1}{4}$

Step-by-step explanation:

Total number of cards in a standard deck = 52

Number of hearts in the deck = 13

Number of clubs in the deck = 13

Number of diamonds in the deck = 13

Number of spades in the deck = 13

Four cards are drawn at random by Timothy.

These four cards are drawn from each one of the suits.

And the cards are not replaced.

Therefore, now cards remaining in each suit:

Remaining number of hearts in the deck = 12

Remaining number of clubs in the deck = 12

Remaining number of diamonds in the deck = 12

Remaining number of spades in the deck = 12

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Here, number of favorable cases are 12 (i.e. number of hearts)

Total number of cases = 12 $\times$ 4 = 48

Therefore, the required probability is:

$\dfrac{12}{48} = \bold{\dfrac{1}4}$