Answer to Question #190925 in Statistics and Probability for Mannan maqsood

Question

5) There are three families each having four children, 2 boys and 2 girls; 3boys and 1 girl; and 1 boy and 3 girls. A child from each family is invited to 

a party. Find the probability  

(i) the only girls turn up for the party?  

(ii) the two girls and one boy turn up for the party? 

Answer 1

We have given that,

Family A have = 2Boys and 2Girls

Family B have = 3Boys and 1Girl.

Family B have = 1Boy and 3Girls.

Single child is selected from each family,

a.)The probability that only girls turn up for the party

$= \dfrac{2}{4} \times \dfrac{1}{4} \times \dfrac{3}{4} = \dfrac{3}{32}$

b.)The probability that two girls and one boy turn up for the party

$= \dfrac{2}{4}.\dfrac{1}{4}.\dfrac{1}{4} + \dfrac{2}{4}.\dfrac{3}{4}.\dfrac{3}{4}+\dfrac{2}{4}.\dfrac{1}{4}.\dfrac{3}{4}$

$= \dfrac{18}{64}+\dfrac{6}{64}+\dfrac{2}{64}$

$= \dfrac{13}{52}$