Probability Question 282
Question: A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is
Options:
A) 8/729
B) 8/243
C) 1/729
D) 8/9
Show Answer
Answer:
Correct Answer: B
Solution:
A pair of fair dice is thrown, the sample space $ S=(1,1),(1,2)(1,3)…=36 $
Possibility of getting 9 are (5, 4), (4, 5), (6, 3), (3, 6)
$ \therefore $ Possibility of getting score 9 in a single throw $ =\frac{4}{36}=\frac{1}{9} $
$ \therefore $ Probability of getting score 9 exactly twice $ {{=}^{3}}C_2\times {{( \frac{1}{9} )}^{2}}.( 1-\frac{1}{9} )=\frac{3!}{2!}\times \frac{1}{9}\times \frac{1}{9}\times \frac{8}{9}=\frac{8}{243} $
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