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.

Answer 1

Hello,

Solution: Given

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

Number of families 475----- 814---- 211

Probability of happening an event

= Favourable outcome/Total Possible Outcome

1) Probability of having two girls:

Favourable cases = 475

Total Possible cases = 1500

Probability = 475/1500 _____eq1

2) Probability of having one girls:

Favourable cases = 814

Total Possible cases = 1500

Probability = 814/1500________eq2

3) Probability of having no girls:

Favourable cases = 211

Total Possible cases = 1500

Probability = 211/1500_________eq3

To check the sum of probabilities= eq1 + eq2 + eq3

=
$\frac{475}{1500} + \frac{814}{1500} + \frac{211}{1500} \\ \\ = \frac{475 + 814 + 211}{1500} \\ \\ = \frac{1500}{1500} \\ \\ = 1$
Hence proved.

Hope it helps you.