Two cards are drawn successively with re

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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Probability Distributions

Question:

Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards, then probability distribution of number of Aces is :

Options:

x	0	1	2
P(x)	$\frac{144}{169}$	$\frac{24}{169}$	$\frac{1}{169}$

x	0	1	2
P(x)	$\frac{1}{169}$	$\frac{2}{169}$	$\frac{4}{169}$

x	0	1	2
P(x)	$\frac{1}{4}$	$\frac{2}{4}$	$\frac{3}{4}$

x	0	1	2
P(x)	$\frac{1}{169}$	$\frac{24}{169}$	$\frac{144}{169}$

Correct Answer:

x	0	1	2
P(x)	$\frac{144}{169}$	$\frac{24}{169}$	$\frac{1}{169}$

Explanation:

The correct answer is Option (1) →

x	0	1	2
P(X)	$\frac{144}{169}$	$\frac{24}{169}$	$\frac{1}{169}$

$P(X=0)=\frac{12}{13}×\frac{12}{13}=\frac{144}{169}$

$P(X=1)=2×(\frac{1}{13}×\frac{12}{13})=2×\frac{12}{169}=\frac{24}{169}$

$P(X=2)=(\frac{1}{13})×(\frac{1}{13})=\frac{1}{169}$

$⇒P(X=0)+P(X=1)+P(X=2)=1$