Question

a family has 3 children. what is the probability of atmost one boy.​

Answer 1

Step-by-step explanation:

Given: A family has 3 children.

To find: What is the probability of atmost one boy.

Solution:

Formula to be implemented:

$\bf Probability \bf =\frac{\text{Favourable response}}{\text{Total response}}$

Step 1: Identify total possibility.

Children can be Boy or Girl(Normally)

Thus,

${2}^{3} = 8$

possibilities are there:

B: Boys and G: Girls

1) BBB

2) BBG

3) BGB

4) BGG

5) GBB

6) GBG

7) GGB

8) GGG

Step 2: Identify favourable cases for atmost one boy.

1) BGG

2) GGB

3) GGG

4) GBG

Step 3: Find probability of family having atmost 1 boy

$P(1B) = \frac{4}{8}$

$P(1B) = \frac{1}{2}$

Final answer:

Probability of family of 3 children having atmost 1 boy is

$\bf P(1B) = \frac{1}{2}$

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Answer 2

Given :  a family has 3 children

To Find :   probability of atmost one boy

Solution:

B = Boy

G = Girl

P(B) = p  = 1/2

P(G) = q  = 1 - p  = 1 - 1/2 = 1/2

n = 3

atmost one boy =>

no boy or 1 boy

Hence x = 0 or  1

P(x) = ⁿCₓpˣqⁿ⁻ˣ

P(atmost one boy)  = P(0) + P(1)

P(0)  = ³C₀(1/2)⁰(1/2)³⁻⁰   = 1/8

P(1)  = ³C₁(1/2)¹(1/2)³⁻¹  =3/8

P(atmost one boy)  =  1/8 + 3/8  = 4/8  = 1/2

probability of atmost one boy  is  1/2

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