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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​?

User Rabin
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1 Answer

2 votes

Answer:

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.

User Jacob Kranz
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