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

Question

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is (A) 1/729 (B) 8/9 (C) 8/729 (D) 8/243

Tardigrade Admin · Accepted Answer

Probability of getting score 9 in a single throw =(4/36)=(1/9) Probability of getting score 9 exactly twice =3C2×((1/9))2×(8/9)=(8/243).

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

$1/729$

$8/9$

$8/729$

$8/243$

Probability of getting score 9 in a single throw $= \frac{4}{36} = \frac{1}{9}$
Probability of getting score 9 exactly twice $=^{3} C_{2} \times (\frac{1}{9})^{2} \times \frac{8}{9} = \frac{8}{243} .$

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

1/729

8/9

8/729

8/243