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vickybarba025

13.01.2022

Mathematics

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.

Step-by-step 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

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

$P=\frac{^{13}C_1}{^{52}C_1}=\frac{13}{52}=0.25$

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

$P(A)=\frac{26}{52}=\frac{1}{2}=0.5$

From the above parts

P(B)=0.25

Total number of black club cards = 13

$P(A\cap B)=\frac{13}{52}=\frac{1}{4}=0.25$

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

$P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}$

$P(\frac{B}{A})=\frac{0.25}{0.5}=0.5$

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

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