# Simple Probability, Sample Spaces, Events

A couple has three children, assume the likelihood of a boy is the same as a girl:

List sample space: {BBB,BBG,BGG,GGG}

Event the children are grils: {GGG}

Event the couple has one or more boy: {BBB,BBG,BGG}

Probability all children are girls: 1/4

Probability the couple has at least one boy: 3/4

Probability the couple has exactly one boy: 1/4

Probability that the couple has two childern of the same gender: 4/4

Knowing that they have one boy, the probability that all the childeren are boys:1/3

Knowing two children are the same gender the probability that they are all boys:1/4

Knowing that two childern are the same gender, the probabilty they have at least two grils:2/4

X -> Random variable of boys couple has -

List all pssoible values of x {0,1,2,3}

PMF of X: 1 = .25, 2 =.25, 3=.25

CDF of X: 1 =.25, 2= .50, 3= .75

Expected Value Of X = 1.5

Expected Value Of X^2 = 3.5

Variance X = 2

Standard Deviation Of X = .42

#### Solution Preview

A couple has three children, assume the likelihood of a boy is the same as a girl:

(a) List sample space: {BBB,BBG,BGG,GGG}

Correct! The sample space has 4 outputs.

(b) Event the children are grils: {GGG}

Correct!

(c) Event the couple has one or more boy: {BBB,BBG,BGG}

Correct!

(d) Probability all children are girls: 1/4

Correct! It is one case in (b) out of the 4 outputs in (a).

(e) Probability the couple has at least one boy: 3/4

Correct!. There are 3 cases in (c) out of the 4 ...

#### Solution Summary

Simple Probability, Sample Spaces, Events are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.