An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :
A
316
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B
12
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C
516
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D
132
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Solution
The correct option is B12 P (odd number twice) =P (even number thrice) ⇒nC2(12)n=nC3(12)n⇒n=5
Success is getting an odd number odd times
Hence P (odd successes) =P(1)+P(3)+P(5) =5C1(12)5+5C3(12)5+5C5(12)5 =1625=12