Question

A card is drawn from a standard deck and replaced. After the deck is shuffled, another card is pulled. What is the probability that the first card drawn is a diamond and the second card is a club?

Answer 1

0.0625 = 6.25% probability that the first card drawn is a diamond and the second card is a club

Explanation:

Answer 2

0.0625 = 6.25% probability that the first card drawn is a diamond and the second card is a club

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Probability of independent events:

The probability of independent events happening at the same time is the multiplication of the probabilities of each events.

First card:

A standard deck has 52 cards, of which 13 are diamonds. So

`P(A) = (13)/(52) = (1)/(4)`

Second card:

The first card is replaced, so still 52 cards, of which 13 are clubs. So

`P(B) = (13)/(52) = (1)/(4)`

What is the probability that the first card drawn is a diamond and the second card is a club?

Each drawing is independent, so

`P(A \cap B) = P(A)*P(B) = (1)/(4)*(1)/(4) = (1)/(16) = 0.0625`

0.0625 = 6.25% probability that the first card drawn is a diamond and the second card is a club