Question

A family has two children. If B represents a boy and G represents a girl, the set of outcomes for the possible genders of the children is S = {BB, BG, GB, GG}, with the oldest child listed first in each pair. Let X represent the number of times G occurs. Which of the following is the probability distribution, PX(x)?

Answer 1

Answer: P(X=0) = 1/4,  P(X=1)=1/2 and  P(X=2)= 1/4.

Step-by-step explanation:

Since, the possible genders of the children is S = {BB, BG, GB, GG}

Here, Let X represent the number of times G occurs.

Thus, when there is no girl

Possible arrangement = {BB}

Then P(X=0) = 1/4

When there is one girl,

Then possible arrangement = { BG, GB}

Thus P(X=1)= 2/4

⇒ P(X=1)=1/2

When there  is 2 girls,

Then possible arrangement = {GG}

Thus P(X=2)= 1/4

Answer 2

Probability helps us to know the chances of an event occurring. The probability distribution of a girl child being born can be drawn as given below.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

Given to us

Possible genders of the children, S = {BB, BG, GB, GG},

We know that the probability of girl child can be found using the formula of probability, now, finding the probability of the girl child,

The probability that there is no girl child born,

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

$P(X=0) = \dfrac{\text{Outcome in which no girl child is born}}{\text{All the possible outcomes}}\\\\P(X=0) = \dfrac{1}{4}\\\\P(X=0) = 0.25$

The probability that there is one girl child is born,

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

$P(X=1) = \dfrac{\text{Outcome in which one girl child is born}}{\text{All the possible outcomes}}\\\\P(X=1) = \dfrac{2}{4}\\\\P(X=1) = 0.5$

The probability that there is two girl child is born,

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

$P(X=2) = \dfrac{\text{Outcome in which two girl child is born}}{\text{All the possible outcomes}}\\\\P(X=2) = \dfrac{1}{4}\\\\P(X=2) = 0.25$

The probability distribution of a girl child being born can be drawn as given below.

Learn more about Probability:

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