A die is rolled a certain number of times. If the probability of getting an odd number 2 times is same as the probability of getting an even number 3 times. The probability of getting an odd number an odd number of times is

A die is rolled a certain number of times. If the probability of getting an odd number 2 times is same as the probability of getting an even number 3 times. The probability of getting an odd number an odd number of times is

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    Solution:

    Let the die be rolled n times. It is given that

     nC212212n2=nC312312n3nC2=nC3n=5

    Let the required probability be p. Then,

    p=5C1121124+5C3123122+5C5125120 p= 5C1+5C3+5C5×132=2425=12

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