Two cards are drawn without replacement.

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Probability

Question:

Two cards are drawn without replacement. The probability distribution of number of aces is given by :

Options:

X	0	1	2
P(X)	$\frac{188}{221}$	$\frac{32}{221}$	$\frac{1}{221}$

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

X	0	1	2
P(X)	$\frac{188}{221}$	$\frac{24}{221}$	$\frac{1}{221}$

X	0	1	2
P(X)	$\frac{188}{221}$	$\frac{1}{221}$	$\frac{24}{221}$

Correct Answer:

X	0	1	2
P(X)	$\frac{188}{221}$	$\frac{32}{221}$	$\frac{1}{221}$

Explanation:

The correct answer is Option (1)

X	0	1	2
P(X)	$\frac{188}{221}$	$\frac{32}{221}$	$\frac{1}{221}$

X → no. of aces drawn

4 → no. of aces

52 → total cards

$P(X=0)=\frac{{^{48}C}_2}{{^{52}C}_2}=\frac{188}{221}$

$P(X=1)=\frac{{^{48}C}_1×{^4C}_1}{{^{52}C}_2}=\frac{32}{221}$

$P(X=2)=\frac{{^{4}C}_2}{{^{52}C}_2}=\frac{1}{221}$