Question

2 cards are chosen from a deck of cards. The first card is replaced before choosing the second card. What is the probability that one card is a club and the other is a heart?

Answer 1

Answer:

The probability that the first card chosen is club and second card chosen is of heart is .

Step-by-step explanation:

Total number of cards in the deck is 52 (total number of cases).

Probability of an event E can be formulated as:

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

For event A, number of cards of type club = 13 (favorable cases)

So,

$P(A) = \dfrac{13}{52} \\\Rightarrow P(A) = \dfrac{1}{4}$

For event B, number of cards of type heart = 13 (favorable cases)

So,

$P(B) = \dfrac{13}{52} \\\Rightarrow P(B) = \dfrac{1}{4}$

It is given that card is replaced before choosing the second card.

These events A and B are independent events, happening of one event does not effect the happening of other.  And probability of both happening together can be found as following:

$P(A \cap B) = P(A) \times P(B)$

$\Rightarrow P(A \cap B) = \dfrac{1}{4} \times \dfrac{1}{4}\\\Rightarrow P(A \cap B) = \dfrac{1}{16}$

The probability that the first card chosen is club and second card chosen is of heart is $\frac{1}{16}$.