From a group of 100 students, 50 study History, 30 study English Literature and 20 study both. If a student is selected at random from the , what is the probability that the student studies.(a) at least one of these subjects.(b) History nut not English Lierature.History, given that the student also studies English Lierature?

Dear student,

since 20 study both,

no. of students study only history = 50-20 = 30

no. of students study only english = 30-20 = 10

=> number of students study atleast one subject = 30+10+20 = 60

probability that student studies atleast one subject = 60/100 = 0.6

probability that student studies history but not english = 10/100 = 0.1

probability that a student studies history given that he studies english = 20/30 = 0.66

i hope it explains