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?
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