# in a family of three children the probability of having at least one boy is

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## In a family of 3 children, find the probability of having at least one boy.

In a family of 3 children, find the probability of having at least one boy.

Byju's Answer Standard X Mathematics

Sum of Probabilities

In a family o... Question

In a family of 3 children, find the probability of having at least one boy.

Open in App Solution

The probability that each child will be a boy is 1/2.

The probability that each child will be a girl is 1/2.

The probability of no. boys = 1/2 × 1/2 × 1/2 = 1/8

The probability of at least 1 boy = 1 - the probability of no boys.

= 1 - 1/8 = 7/8 or

The number of the possibilities is shown below

Probability of 0 boys = 1/8

Probability of 1 boy = 3 × 1/8 = 3/8

Probability of 2 boys = 3 × 1/8 = 3/8

Probability of 3 boys = 1/8

The probability of at least 1 boy is equal to the probability of 1 or 2 or 3

boys which = 3/8 + 3/8 + 1/8 = 7/8.

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SIMILAR QUESTIONS

**Q.**In a family of 3 children, find the probability of having at least one boy.

**Q.**A family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

**Q.**Mark the correct alternative in each of the following:

In a family of 3 children, the probability of having at least one boy is

(a) 78 (b) 18 (c) 58 (d) 34 [CBSE 2014]

**Q.**One family has been chosen out of 200 families having 3 children . What is the probability that there is at least one girl ?

**Q.**If atleast one child in a family with

3

children is a boy then the probability that

2

of the children are boys, is

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Sum of Probabilities

Standard X Mathematics

## In a family of 3 children, find the probability of having at least 1 boy.

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Question

## In a family of 3 children, find the probability of having at least 1 boy.

In a family of 3 children, to find the probability of having at least 1 boy, let us find the probability of no boy.Easy Open in App Solution Verified by Toppr

The sample space for different cases contains 2

3

=8 points. [ As there are 3 children and the child may be boy or a girl] among which there is only one case when there are all girls that means no boy.

So probability of no boy is

8 1 .

So the probability of at least one boy is 1−

8 1 = 8 7 .

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## In a family of 3 children, find the probability of having at least one boy.

In a family of 3 children, find the probability of having at least one boy.. Ans: Hint: We will first start by assuming that the boy is represented by B and girl by G. Then we will find the total possible outcomes of having at least one boy and then ...

## In a family of 3 children, find the probability of having at least one boy.

Last updated date: 13th Mar 2023

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Hint: We will first start by assuming that the boy is represented by B and girl by G. Then we will find the total possible outcomes of having at least one boy and then we will use the fact that probability of an event is the total favourable outcomes divided by total possible outcomes.

Complete step-by-step answer:

Now, we have been given that a family has 3 children and we have to find the probability of at least one boy.

Now, let us assume that the boy is represented by B and girl by G. So, we have the total favourable outcomes as,

I. BBB II. BBG III.BGG IV.BGB V. GGB VI. GBB VII. GBG VIII.GGG

Now, we have total 8 cases as listed above for 3 children. Now, for favourable cases we have to find the cases in which there is atleast one boy. So, there must be at least one or more boy.

Now, for this scenario we have 7 cases in which there are one or more boys.

Now, we know that for the probability of an event

=

Number of favourable outcomes

Number of total possible outcomes

=Number of favourable outcomesNumber of total possible outcomes

= 7 8 =78

Probability of having at least one boy is

7 8 78 .

Note: It is important to note that there are 8 outcomes for the given situation. Children might think that there are four events in total as 3 boys, 1 girl, 2 boys, 2 girls, 1 boy, 2 girls and the probability of each of these are equal but this is wrong. As for this we have to make assumptions that would lead to contradiction.

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