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Chapter 15: Q13P (page 728)

A student claims in Problem 1.5 that if one child is a girl, the probability thatboth are girls is 12. Use appropriate sample spaces to show what is wrong withthe following argument: It doesn’t matter whether the girl is the older child or theyounger; in either case the probability is 12that the other child is a girl.

Short Answer

Expert verified

The probability of the second child being a girl is13 when another child is a girl.

Step by step solution

01

Definition of Sample Space

Sample space of any experiment is the set of all possible mutually exclusive events.Sample space can be uniform or non-uniform, it depends on the probability of each event in the sample space.

02

Creation ofsample space

A child being a girl or a boy does not depend on whether the previous child was a girl or a boy.

Let G represents girl child and B represents Boy child, so, the possible outcomes for two children are 4 that are as follows,

BB , BG , GB , GG

03

Analysing the argument

When one child is a girl, this makes out of the events and the sample space becomes BG , GB , GGand each has a probability of 13, this implies that the probability of other child being a girls is13 when the other child is also a girl.

Thus, the given argument is incorrect.

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