Three children are selected at random from a group of 6 boys and 4 girls.

Question

Three children are selected at random from a group of 6 boys and 4 girls. It is known that in this group exactly one girl and one boy belong to same parent. The probability that the selected group of children have no blood relations, is equal to

Options:

A . 115

B . 1315

C . 1415

D . 215

Answer: Option C
:
C
P(boyand his sister both are selected) =

\frac{8 C_{1}}{10 C_{3}} = \frac{1}{15}

∴

required probability =

1 - \frac{1}{15} = \frac{14}{15}

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