Question

Suppose that a single card is selected from a standard​ 52-card deck. What is the probability that the card drawn is a clubclub​?

Now suppose that a single card is drawn from a standard​ 52-card deck, but it is told that the card is blackblack. What is the probability that the card drawn is a clubclub​?

Answer 1

The probability that the card drawn is a club is 0.25.

The probability that card drawn is a club, when it is given that the card is black is 0.5.

Explanation:

In a standard​ deck of cards:

Total number of cards = 52

Total number of cards of each suit (club, spade,heart, diamond) = 13

The probability that the card drawn is a club is

`P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}`

`P=(^(13)C_1)/(^(52)C_1)=(13)/(52)=0.25`

Therefore the probability that the card drawn is a club is 0.25.

Let A and B represents the following events:

A : Card is black

B : Card is a club

Total number of black cards = 26

`P(A)=(26)/(52)=(1)/(2)=0.5`

From the above parts

`P(B)=0.25`

Total number of black club cards = 13

`P(A\cap B)=(13)/(52)=(1)/(4)=0.25`

We need to find the probability that card drawn is a club, when it is given that the card is black.

`P((B)/(A))=(P(A\cap B))/(P(A))`

`P((B)/(A))=(0.25)/(0.5)=0.5`

Therefore the probability that card drawn is a club, when it is given that the card is black is 0.5.