Question

(2 points) The STAT 213 final exam is scheduled to be on Wednesday April 29, 2020 @ 12pm-2pm. However, the number of students who know this is limited. Say only 36% of students know this. A worried prof askes a number of students the following question Do you know when the inal exam for this class will be (a) What is the probability that the 99h student selected will be the 27th student to respond YES? 001232 (use five decimals in your answer) it may also be useful to know that deferred final exams can only be granted by the registrar and not by your instructor

Answer 1

Only 36% of the students know about the final exam.

A worried prof asks a number of students about the timing of the final exam.

We have to find the probability that the 99th student will be the 27th student to respond YES.

Now, the chance of a student saying YES is 0.36.

So, the chance of a student saying NO is 1-0.36=0.64.

So, if the 99th is the 27th student to say YES, that means, 26 out of the previous 98 students said YES. We can select those 26 out of 98 in (98 C 26) ways. The probability of these 26 saying YES is (0.36*0.36*0.36*.....26 times).

The chance of the rest (98-26)=72 saying NO is (0.64*0.64*0.64*....72 times).

And the probability of the 99th one saying YES is another 0.36.

So, the required probability is

=(98 C 26)(0.36)26*(0.64)72*0.36

=0.0044.

So, the required probability is 0.0044.