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Assuming that boy and girl babies are equally likely, what would be Kathy's probability of having at most one daughter if she
were to have four children altogether? (You may want to use a tree diagram to construct the sample space.)
The probability is
(Type an integer or a simplified fraction.)

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WonderlandWanderer

Answer: 0.3125.

Step-by-step explanation:

  • The chance of having a boy is 0.5,
  • the chance of having a girl is also 0.5.

Outcome 1: all boys

boy  boy  boy  boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Outcome 2: first child is a girl, all others are boys

girl   boy   boy   boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Outcome 3: second child is a girl, all others are boys

boy   girl   boy   boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Outcome 4: third child is a girl, all others are boys

boy   boy   girl   boy

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Outcome 5: fourth child is a girl, all others are boys

boy   boy   boy   girl

0.5 * 0.5 * 0.5 * 0.5 = 0.0625

Therefore,

0.0625 + 0.0625 + 0.0625 + 0.0625 + 0.0625 = 0.0625 * 5 = 0.3125

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