## Book: Mathematics Part-II

### Chapter: 13. Probability

#### Subject: Maths - Class 12th

##### Q. No. 12 of Exercise 13.1

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12
##### Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?

Let B denote boy and G denote girl.

Then, the sample space of the given experiment will be:

S = {GG, GB, BG, BB}

Let E be the event that ‘both are girls’.

E = {GG} (i) Let F be the event that ‘the youngest is a girl’.

F = {GG, BG} ……….(I)

Now, E F = {GG} ……….(II)

Now, we know that

By definition of conditional probability,  [Using (I) and (II)] (ii) Let H be the event that ‘at least one is a girl’.

H = {GG, GB, BG} ……….(III)

Now, E H = {GG} ……….(IV)

Now, we know that

By definition of conditional probability,  [Using (III) and (IV)] 12

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