A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
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a
8/729
b
8/243
c
1/729
d
8/9
answer is B.
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Detailed Solution
A pair of fair dice is thrown, the sample space S=(1, 1),(1, 2)(1, 3)……. =36 ∴ Possibility of getting score 9 in a single throw = 436=19 ∴ probability of getting score 9 exactly twice =3C2×(19)2.(1−19)=3!2!×19×19×89 =3.2!2!×19×19×89=8243