Question

A survey was conducted on 300 families having 2 children each. The results obtained are given below.

Number of girl child	2	1	0	Total
Number of families	95	165	40	300

If one family is selected at random, find the probability that it will have:

1. one girl child
2. one or more girl child
3. no boy child

Answer 1

(a) Total number of families = 300

Let E be the event of selecting family with one girl child.

∴ Number of favorable outcomes = 165

P(E) = `"Number of favorable outcomes"/"Total number of outcomes"`

= `165/300`

= `11/20`

(b) Let A be the event of selecting a family with one or more girl child.

∴ Number of favorable outcomes = 165 + 95

= 260

P(A) = `"Number of favorable outcomes"/"Total number of outcomes"`

= `260/300`

= `13/15`

(c) Let B be the event of selecting a family with no boy child.

A family will have no boy child if there are 2 girl children in the family.

∴ Number of favourable outcomes = 95

P(B) = `"Number of favorable outcomes"/"Total number of outcomes"`

= `95/300`

= `19/60`