Question

11. Out of 4000 families with 5 children each how many would you expect
to have (a) at least 1 boy (b) 2 boys (C) 1 or 2 girls (d) no girls.
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Answer 1

Step-by-step explanation:

So we are considering families with 4 children. We can take the gender of the children is following binomial distribution with probability of being boy= probability of being girl= 1/2

(1)

probability of atleast 1 boy= 1 - (probability all girls)

= 1 - (1/2)^4

=1 - 1/16

=15/16

So expected no. of families with that criteria, from a pool of 2000 families= 15/16 * 2000=1875

(2)

probability of 1 girl = 4c1*(1/2)*(1/2)^3=1/4

probability of 2 girls = 4c2*(1/2)^2 * (1/2)^2= 3/8

So the OR of the above = (1/4)+(3/8)=5/8

So again, expected no. of families with that criteria = 5/8 * 2000 = 1250