A family has n children with probability ?pn,n ? 1, where

Chapter 4, Problem 14P

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QUESTION:

Problem 14P

A family has n children with probability αpn,n ≥ 1, where α ≤ (1 − p) /p.

(a) What proportion of families has no children?

(b) If each child is equally likely to be a boy or a girl (independently of each other), what proportion of families consists of k boys (and any number of girls)?

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QUESTION:

Problem 14P

A family has n children with probability αpn,n ≥ 1, where α ≤ (1 − p) /p.

(a) What proportion of families has no children?

(b) If each child is equally likely to be a boy or a girl (independently of each other), what proportion of families consists of k boys (and any number of girls)?

ANSWER:

Solution:

Step 1 of 3:

A family has n children with probability , 1, where (1-p)/p.

  1. We have to find what proportion of families has no children.
  2. We have to find the proportion of families consists of k boys, if each child is likely to be a boy or a girl.

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