A professor won USD 1 million playing poker in las Vegas during spring break. At

Question

A professor won USD 1 million playing poker in las Vegas during spring break. At his return he wants to help, and creates a scholarship program for the top 7 University freshmen students. In essence, the professor splits the money in 4 different funding-level fellowships. Each student can only be awarded 1 fellowship.

a) Please explain how would you estimate the different ways in which the fellowships could be awarded? Estimate the number.

b) Under the assumption that the simple events are equally likely (each student has the same probability of being awarded a fellowship), find the probability that student No. 2 is awarded one.

c) Suppose students 5 and 6 have submitted proposals, if the fellowships are awarded at random by the professor, find the probability that both of these students receive fellowships.

Explanation / Answer

Total different funding levels = 4

Program is for top 7 university freshmen.

a) Different number of ways in which the felloships could be awarded is = 7C4( as there is to be distributes 4 fellowships amoung 7 students) = 28

b)

Probability that student no.2 is awarded one is = 4/7 = 0.5714

c)

probability of both 5 and 6 to be awarded feollowships is = 4/7 * 4/7 = 0.3265

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