Question

A particular professor is known for his arbitrary grading policies. eachpaper receives a grade from the set{a, a-, b+, b, b-, c+}, with equalprobability, independently of other papers. how many papers do youexpect to hand in before you receive each possible grade at least once?

Answer 1

Answer:

The answer to the question is;

The number of papers expected to be handed in before receiving each possible grade at least once is 14.93.

Step-by-step explanation:

To solve the question , we note that it is a geometric distribution question which have equal probabilities and therefore is a form of Binomial distribution with Bernoulli trials, where we are conducting the trials till we have r successes

Since we have r = 6, we will have to find the expected value of the number of trials till the nth paper handed in receives a previously awarded grade.

We therefore have,

The Probability that out of six papers turned 5 are different scores is given by

P(Y=5) = p'= q⁵p = (1-p)⁵p = 3125/46656

Therefore p' = the probability of receiving different grades once then the expected value is given by

E(X)  = 1/p' = 46656/3125 = 14.93.