A pair of fair dice is thrown independently three times. probability of getting a score of exactly 9

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14.Probability

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A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is

A

$\frac{8}{{729}}$

B

$\frac{8}{{243}}$

C

$\frac{1}{{729}}$

D

$\frac{8}{9}$

(AIEEE-2007)

Solution

Probability of getting score $9$ in a single throw

$=\frac{4}{36}$

$=\frac{1}{9}$

Probability of getting score $9$ exactly twice

$=3 C_{2} \times\left(\frac{1}{9}\right)^{2} \times \frac{8}{9}$

$=\frac{8}{243}$

Standard 11

Mathematics

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