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From a group of 3 girls and 2 boys, two children are selected at random, then the probability such that at least one boy is selected is

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913

710

313

1013

answer is B.

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Detailed Solution

Given that there is a group of 3 girls and 2 boys.
Let the girls be G1, G2, G3 and boys be B1, B2.
Total ways of selection =

5 C 2

5 C 2 = 5 × 4 × 3 × 2 × 1 2 × 1 × 3 × 2 × 1 = 5 × 4 2 = 10

Sample space where at least one boy is there,
S = {(B1, G1), (B1, G2), (B1, G3), (B2, G1), (B2, G2), (B2, G3), (B1, B2)}
Hence n(S) = 7.
∴The probability such that at least one boy is selected

= n (S) T o t a l ways of selection = 710

The probability such that at least one boy is selected is

710

.
Therefore, option 2 is correct.

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