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.

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*) = 2^{4} = 16.

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

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

Step 2

**Find the probability of getting four girls and no boys:**

The number of favourable elements under the events 4*G *and 0*B *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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