Mathematics: Are these questions different at all? And if so whats the answer to them?

Are these questions different at all? And if so

vickybarba025

13.01.2022

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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