Two dice are thrown simultaneously. If X

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Probability

Question:

Two dice are thrown simultaneously. If X denotes the number of fours, then the expectation of X will be:

Options:

$\frac{5}{9}$

$\frac{1}{3}$

$\frac{4}{7}$

$\frac{3}{8}$

Correct Answer:

$\frac{1}{3}$

Explanation:

The correct answer is Option (2) - $\frac{1}{3}$

$X$	0	1	2
$P(X)$	${^2C}_0(\frac{5}{6})^2=\frac{25}{36}$	${^2C}_1(\frac{1}{6})(\frac{5}{6})=\frac{10}{36}$	${^2C}_2(\frac{1}{6})^2=\frac{1}{36}$

$E(X)=0×\frac{25}{36}+1×\frac{10}{36}+2×\frac{1}{36}$

$=\frac{10+2}{36}=\frac{1}{3}$