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​

Answer 1

Solution :-

Total number of families = 1500

(i) ∵ Number of families having 2 girls = 475

∵ Probability of selecting a family having 2 girls

⠀⠀⠀⠀⠀ = $\dfrac{475}{1500}$= $\dfrac{19}{60}$

(ii) ∵ Number of families having 1 girl = 814

∴ Probability of selecting a family having 1 girl

⠀⠀⠀⠀⠀= $\dfrac{814}{1500}$= $\dfrac{407}{750}$

(iii) Number of families having no girl = 211

Probability of selecting a family having no girl

⠀⠀⠀⠀⠀ = $\dfrac{211}{1500}$

Now, the sum of the obtained probabilities

⠀⠀⠀⠀⠀= $\dfrac{19}{60}$ + $\dfrac{475}{1500}$ + $\dfrac{211}{1500}$

⠀⠀⠀⠀⠀= $\dfrac{475+814+211}{1500}$

⠀⠀⠀⠀⠀= $\dfrac{1500}{1500}$

⠀⠀⠀⠀⠀= 1

i.e., Sum of the above probabilities is 1.