Randomly meeting a four child family with either one or exactly 2 boy children

The probability of randomly meeting a four child family with either exactly one or exactly two boy children = (5/8) = 0.625

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Complete Question

The probability of randomly meeting a four child family with either exactly one or exactly two boy children.

Solution

The possible sample spaces for a family with four children include

4 boys and 0 Girl

3 boys and 1 girl

BBBG BBGB BGBB GBBB

2 boys and 2 girls

BBGG BGBG BGGB GBBG GBGB GGBB

1 boy and 3 girls

BGGG GBGG GGBG GGGB

0 boy and 4 girls

Total number of elements in the sample space = 16

Probability of an event is defined as the number of elements in that event divided by the Total number of elements in the sample space.

The required probability is a sum of probabilities.

The probability of meeting a four child family with exactly 1 boy = (4/16) = (1/4) = 0.25

The probability of meeting a four child family with exactly 2 boys = (6/16) = (3/8) = 0.375

The probability of randomly meeting a four child family with either exactly one or exactly two boy children = (4/16) + (6/16) = (10/16) = (5/8) = 0.25 + 0.375 = 0.625

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