Question

You select a family with four children. If M represents a male child and F represents a female​ child, the set of equally likely outcomes for the​ children's genders is​ {FFFF, FFFM,​ FFMF, FMFF,​ MFFF, MFFM,​ MFMF, MMFF,​ FFMM, FMFM,​ FMMF, FMMM,​ MFMM, MMFM,​ MMMF, MMMM}. Find the probability of selecting a family with exactly one male child.

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Answer 1

The probability of selecting a family with exactly one male child is 1/16

Explanation:

As given the family of four children. Total possible outcomes are

{FFFF, FFFM,​ FFMF, FMFF,​ MFFF, MFFM,​ MFMF, MMFF,​ FFMM, FMFM,​ FMMF, FMMM,​ MFMM, MMFM,​ MMMF, MMMM}

Possible outcome with one male child are {FFFM,​ FFMF, FMFF,​ MFFF}

Total = 16

With 1 male = 4

Probability (P) of one male = 4/16

P = 1/16

Answer 2

The probability of selecting a family with exactly one male child is 1/4 or 0.25.

Explanation:

Given in the question,

possible outcomes for the children's genders

{FFFF, FFFM,​ FFMF, FMFF,​ MFFF, MFFM,​ MFMF, MMFF,​ FFMM, FMFM,​ FMMF, FMMM,​ MFMM, MMFM,​ MMMF, MMMM}

= 16

To find,

the probability of selecting a family with exactly one male child

Probability = favourable outcomes / possible outcomes

favourable outcomes = {FFFM,​ FFMF, FMFF,​ MFFF}

= 4

Probability = 4 / 16

= 1 / 4

= 0.25