At a certain university, 20% of students only major in literature, 15% of studen

Question

At a certain university, 20% of students only major in literature, 15% of students only major in history, and 8% of students major in both literature and history. The literature-only majors spend a semester abroad with probability 0.32, the history-only majors spend a semester abroad with probability 0.49, and the literature-history double-majors study abroad with probability 0.93. Students of other majors study abroad with probability 0.04. If a student from this university spends a semester studying abroad, what is the probability he or she is a double-major in literature and history?

Explanation / Answer

here let the event a student goes abroad =A,

for student major in literature =Ml; history =Mh, both =Mlh and others =Mo

as probabilty of other major student =Mo=1-0.2-0.15-0.08 =0.57

hence probabilty of going abroad P(A)=P(Ml)*P(A|Ml)+P(Mh)*P(A|Mh)P(Mlh)*P(A|Mlh)+P(Mo)*P(A|Mlo)

=0.2*0.32+0.15*0.49+0.08*0.93+0.57*0.04 =0.2347

therefore probabilty that one is major literature and history,given he goes abroad =P(Mlh|A) =P(Mlh)*P(A|Mlh)/P(A)

=0.08*0.93/0.2347 =0.317

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