Question

An instructor has a question bank consisting of 300 easy True / False questions. 200 difficult True / False questions. 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the

Answer 1

Clearly, the sample space cosists of 1400 quations.
`:. n(S)=1400`
Let `A=` event of selecting an easy question, and
`B=` event of selecting a multiple - choice question.
Then, `A nn B=` event of selecting an easy multiple-choice question.
`:. n(A)=(300+500)=800, n(B)=(500+400)=900`
and `n(A nn B)=500`.
So, `P(A)=(n(A))/(n(S))=800/1400=4/7, P(B)=(n(B))/(n(S))=900/1400=9/14`
and `P(A nn B)=(n(A nn B))/(n(s))=500/1400=5/14`
Suppose b has already occurred and then A occurs.
Thus we have to find `P(A//B)`.
Now, `P(A//B)=(P(Ann B))/(P(B))=((5//14))/((9//14))=(5/14xx14/9)=5/9`.
Hence, the required probability is `5/9`.