#### Question

1500 families with 2 children were selected randomly, and the following data were recorded:-

Number of girls in a family | 2 | 1 | 0 |

Number of families | 475 | 814 | 211 |

Compute the probability of a family, chosen at random, having

(i) 2 girls (ii) 1 girl (iii) No girl

Also check whether the sum of these probabilities is 1.

#### Solution

Total number of families = 475 + 814 + 211

= 1500

(i) Number of families having 2 girls = 475

`P_1"(a randomly chosen family has 2 girls) "="Number of families having 2 girls"/"Total number of families"=475/1500=19/60`

(ii) Number of families having 1 girl = 814

`P_2"(a randomly chosen family has 1 girl) "="Number of families having 1 girl"/"Total number of families"=814/1500=407/750`

(iii) Number of families having no girl = 211

`P_3"(a randomly chosen family has no girl) "="Number of families having no girl"/"Total number of families"=211/1500`

`"Sum of all these probabilities "=19/60+407/750+211/1500`

`=(475+814+211)/1500`

`=1500/1500=1`

Therefore, the sum of all these probabilities is 1.