Question

6. In a family of two children , a child is selected at random . Find the

probability of

(i) Both are boys.​

Answer 1

Answer:

find P (both children are males, if it is known that at least one of the children is male).

A: Event that both children are male, and B: event that at least one of them is a male.

A: {MM} and B: {MF, FM, MM} →→ P (A ∩∩ B) = {MM}

Probability that both are males, if we know one is a female =P(A/B)=P(A∩B)/P(B)

(P(A∩B)P(B))

Given S = {MM, MF, FM, FF}, we can see that: P (A) = 1414; P (B) = 3434; P (A ∩∩ B) = 1414

Therefore P(B/A)=P(A∩B)/P(A) =(1/4)/(3/4)=1/3

Answer 2

am starting with the assumption that we are selecting from the population of ALL families, not just the ones that have boys.

In the first method, I am assuming that we are randomly choosing one child from the family that we selected, and observing that child, but not the other.

The possibilities are:

BB

BG

GB

GG

When we observe a child at random, each of these eight children has an equal chance of being the one

we saw.

We make our observation, and the child we see is a boy.

I think it will be helpful to you ☺️

nice to meet you