Mathematics, 17.06.2020 22:57 jeremiahhart13

To the right are the outcomes that are possible when a couple has three children. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly 1 boy. 1st 2nd 3rd boy minus boy minus boy boy minus boy minus girl boy minus girl minus boy boy minus girl minus girl girl minus boy minus boy girl minus boy minus girl girl minus girl minus boy girl minus girl minus girl What is the probability of exactly 1 boy out of three children?

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Answer from: Tcareyoliver

There is 37.5% probability of exactly 1 boy out of three children.

Given that,

To the right are the outcomes that are possible when a couple has three children.

Assume that boys and girls are equally likely, so that the eight simple events are equally likely.

We have to find,

The probability that when a couple has three children, there is exactly 1 boy.

According to the question,

A probability is the number of desired outcomes divided by the number of total outcomes.

The possible outcomes are:

The b denote the boy,

And g denote the girl

Therefore,

b - b - b

b - b - g

b - g - b

b - g - g

g - b - b

g - b - g

g - g - b

g - g - g

There are 8 possible outcomes.

The probability that when a couple has three children, there is exactly 1 boy.

b - g - g

g - b - g

g - g - b

There are 3 outcomes for exactly 1 boy.

Therefore,

The probability of exactly 1 boy out of three children is given by,

$= \dfrac{ 3 \ outcomes\ for \exacatly\ 1 \ boy}{total \ possible \ outcomes }\\\\= \dfrac{3}{8}\\\\= 0.375\\\\= 37.5\ percent$

Hence, There is 37.5% probability of exactly 1 boy out of three children.

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Answer from: Maddi7328

37.5% probability of exactly 1 boy out of three children

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The possible outcomes are:

b for boy, g for girl

b - b - b

b - b - g

b - g - b

b - g - g

g - b - b

g - b - g

g - g - b

g - g - g

There are 8 possible outcomes.

Exactly one boy:

b - g - g

g - b - g

g - g - b

3 outcomes

What is the probability of exactly 1 boy out of three children?

3/8 = 0.375

37.5% probability of exactly 1 boy out of three children

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