Assume that the birth of a boy or girl to a couple to be equally likely, mutually exclusive, exhaustive and independent of the other children in the family. For a couple having `6` children, the probability that their "three oldest are boys" is

Options

A. `(20)/(64)`
B. `(1)/(64)`
C. `(8)/(64)`
D. none of these

Answer

C

Explanation

`(c )` `E : B_(1)B_(2)B_(3)xxxxxx`, where `xx` means `B` or `G`
`:.P(E)=(1)/(2)*(1)/(2)*(1)/(2)=(1)/(8)=(8)/(64)`