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

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

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) = \frac{\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) = (13)/(52) \\\Rightarrow P(A) = (1)/(4)`

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

So,

`P(B) = (13)/(52) \\\Rightarrow P(B) = (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) * P(B)`

`\Rightarrow P(A \cap B) = (1)/(4) * (1)/(4)\\\Rightarrow P(A \cap B) = (1)/(16)`

The probability that the first card chosen is club and second card chosen is of heart is
`(1)/(16)`.