The sample space listing the eight simple events that are possible when a couple has three children is​ {bbb, bbg,​ bgb, bgg,​ gbb, gbg,​ ggb, ggg}. After identifying the sample space for a couple having four​ children, find the probability of getting fourfourgirlsgirlsand nonoboysboys.Identify the sample space for a couple having four children. ​{nothing​}​(Use a comma to separate answers as​ needed.)Find the probability of getting fourfourgirlsgirlsand nonoboysboys.

Question
Asked Feb 21, 2019
The sample space listing the eight simple events that are possible when a couple has three children is {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. After identifying the sample space for a couple having four children, find the probability of getting
fourfour
girlsgirls
and
nono
boysboys.
Identify the sample space for a couple having four children.
 
{nothing}
(Use a comma to separate answers as needed.)
Find the probability of getting
fourfour
girlsgirls
and
nono
boysboys.
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Expert Answer

Step 1

Identify the sample space for a couple having four children:

Sample space:

The set of all possible outcomes of a probability experiment is called sample space of the experiment.

Here, the couple have four children. The events having a girl child and having a boy child are equally likely.

That is, the probability of having a boy child and girl child is same.

Each outcome will have 4 elements and each of the 4 elements is equally likely and independent.

Let G represents girl child and B represents boy child.

The total number of outcomes in the sample space be n(S) = 24 = 16.

The possible outcomes will be 4G and 0B, 3G and 1B, 2G and 2B, 1G and 3B, 0G and 4B.

The sample space for a couple having four children is given below:

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Step 2

Find the probability of getting four girls and no boys:

The number of favourable elements under the events 4G and 0B is only 1.

The total number of outcomes in the sample space is 16.

The probability of getting four girls and no boys is obtained as 0....

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