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Question

Mathematics Question on binomial distribution

A die is thrown 1010 times, the probability that an odd number will come up at least one time is

A

11024\frac{1}{1024}

B

10231024\frac{1023}{1024}

C

111024\frac{11}{1024}

D

10131024\frac{1013}{1024}

Answer

10231024\frac{1023}{1024}

Explanation

Solution

Given n=10n =10
Probability of odd number, p=1/2p =1 / 2
∴q=1/2\therefore q =1 / 2
Required probability =P(X≥1)= P ( X \geq 1)
=1−P(X=0)=1- P ( X =0)
=1− 10C0(1/2) 10−0(1/2)0= 1- \,^{10}C_0 (1/2)\,^{10-0}(1/2)^0
=1−1/210=1-1 / 2^{10}
=1−1/1024=1-1 / 1024
=1023/1024=1023 / 1024