Q. 24

A class consists of 10 boys and 8 girls. Thee students are selected at random. What is the probability that the selected group has (i) all boys? (ii) all girls? (iii) 1 boy and 2 girls? (iv) at least one girl? (v) at most one girl?

Answer :

given: class consisting of 10 boys and 8 girls


formula:


three students are selected at random, total possible outcomes are 18C3


therefore n(S)=18C3


= 816


(i) let E be the event that all are boys


n(E)= 10C3


=120





(ii) let E be the event that all are girls


n(E)= 8C3


=56





(iii) let E be the event that one boy and two girls are selected


n(E)= 8C110C2=360




(iv) let E be the event that at least one girl is in the group


E= {1,2,3}


n(E)= 8C110C2+8C210C1+8C310C0=696




(v) let E be the event that at most one girl is in the group


E= {0, 1}


n(E)= 8C010C3+8C110C2=480




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