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

Result:

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?

L: literature   H: history   LH: literature and history O: Others A: abroad

P( L) = 0.20   P(H)= 0.15    P(LH)=0.08   P(O) =0.57

P( A/L) = 0.32 P(A/H) = 0.49    P(A/LH)=0.93   P(O) =0.04

Bayes theorem used

P(A) = P( A/L)* P( L)+ P( A/H)* P( H)+ P( A/LH)* P( LH)+ P( A/O)* P( O)

=0.32*0.20+0.49*0.15+0.93*0.08+0.04*0.57

=0.2347

P(LH/A) = P( A/LH)* P( LH)/P(A)

=0.93*0.08/0.2347

=0.317000426

The required probability = 0.3170

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