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Chapter 4: Q. 4.45 (page 166)

A student is getting ready to take an important oral examination and is concerned about the possibility of having an “on” day or an “off” day. He figures that if he has an on the day, then each of his examiners will pass him, independently of one another, with probability8, whereas if he has an off day, this probability will be reduced to4. Suppose that the student will pass the examination if a majority of the examiners pass him. If the student believes that he is twice as likely to have an off day as he is to have an on the day, should he request an examination with3examiners or with5examiners?

Short Answer

Expert verified

The probability of passing is more, if 3examiners, So he should prefer 3examiners.

Step by step solution

01

Given Information

A student is getting ready to take an important oral examination and is concerned about the possibility of having an “on” day or an “off” day.

Probability of off day =23

Probability of on day=13.

02

Solution of the Problem

If he request 3Examiners then:

P[pass if2or more emaminers pass him]

=2332(0.4)2·(0.6)+33(0.4)3+1332(0.8)2·(0.2)+33(0.8)3

=23[0.288+0.064]+13[0.384+0.512]

We get,

=0.2347+0.2987

=0.533.

03

Computation of the Probability

If he request 5Examiners then:

P[pass if3or more examiners pass him]

P(pass)=2353(0.4)3·(0.6)2+54(0.4)4·(0.6)+55(0.4)5

+1353(0.8)3·(0.2)2+54(0.8)4·(0.2)+55(0.8)5

We get,

=23[0.2304+0.0768+0.01024]+13[0.2048+0.4096+0.32768]

=0.2117+0.314

=0.526

04

Final Answer

The probability of passing is more, if 3examiners, So he should prefer 3examiners.

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Most popular questions from this chapter

Five men and 5 women are ranked according to their scores on an examination. Assume that no two scores are alike and all 10! possible rankings are equally likely. LetXdenote the highest ranking achieved by a woman. (For instance,X=1 if the top-ranked person is female.) FindP{X=i},i=1,2,3,…,8,9,10

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