Suppoce a couple has four children. Assume that each child is equaly kely to be a boy or a girl, regardess of the outcome of previous births. The falowing tae shows the reuts of simultcen todetermine the gencer breakdown in 20 tamliesNumber of girts34.곯-0.1 | -0.2 | 옮-0.3Probabilty202020-0.3-0.1Baned on the simulation results, which mere kely,a 2:2 solt of boys and grts ora 3:1 soit in ether drecton?Uspit is mare lkely with a probaany ofb. Wte out the sampe space and calcuate the exact probabiities for the varius pesble gender breakdownsEnter the exact answer as a decmal.Number of ges23Probabitye Rearwer parta uning eact probabtiesspit more lieely with a probablity of

Given data: Probability distribution of number of girls: Number of girls 0 1 2 3 4 Probability…

Answered: Suppoce a couple has four children.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Suppoce a couple has four children. Assume that each child is equaly kely to be a boy or a girl, regardess of the outcome of previous births. The falowing tae shows the reuts of simultcen to
determine the gencer breakdown in 20 tamlies
Number of girts
3
4.
곯-0.1 | -0.2 | 옮-0.3
Probabilty
20
20
20
-0.3
-0.1
Baned on the simulation results, which mere kely,a 2:2 solt of boys and grts ora 3:1 soit in ether drecton?
Uspit is mare lkely with a probaany of
b. Wte out the sampe space and calcuate the exact probabiities for the varius pesble gender breakdowns
Enter the exact answer as a decmal.
Number of ges
2
3
Probabity
e Rearwer parta uning eact probabties
spit more lieely with a probablity of

Expert Solution

Step 1

Given data:

Probability distribution of number of girls:

Number of girls	0	1	2	3	4
Probability	0.10	0.20	0.30	0.30	0.10

Step 2

(a)

2:2 split of boys and girls means two girls and two boys. So, the probability of 2 boys and 2 girls is equal to probability of 2 girls:

$\begin{array}{rcl} P (2 b o y s a n d 2 g i r l s) & = & P (2 g i r l s) \\ = & 0.30 \end{array}$

3:1 split of boys and girls means three boys and one girl or one boy and three girls. So, the probability is equal to sum of probability of 1 girl and probability of 3 girl.

$\begin{array}{rcl} P (3 b o y s a n d 1 g i r l o r 1 b o y a n d 3 g i r l s) & = & P (1 g i r l) + P (3 g i r l s) \\ = & 0.20 + 0.30 \\ = & 0.50 \end{array}$

From the above results, it is clear that 1:3 split is more likely than 2:2 split.

Thus, 1:3 split is more likely with a probability of 0.50.

(b)

Since there are 4 children so the total number of possible outcomes will be $2^{4} = 16 .$

The sample space of this experiment is given as:

$S = \{G G G G, G B G G, B G G G, B B G G G G G B, G B G B, B G G B, B B G B G G B G, G B B G, B G B G, B B B G G G B B, G B B B, B G B B, B B B B\}$

Now, compute the EXACT probability of the following classification of each number of girls:

Number of girls	Possible outcomes	Probability
0	BBBB	$\frac{1}{16} = 0.0625$
1	BBGB, BBBG, GBBB, BGBB	$\frac{4}{16} = 0.25$
2	BBGG, GBGB, BGGB, GBBG, BGBG, GGBB	$\frac{6}{16} = 0.375$
3	GBGG, BGGG, GGGB, GGBG	$\frac{4}{16} = 0.25$
4	GGGG	$\frac{1}{16} = 0.0625$