Question

probabilty students have pencil is 0.40.

a) probability that at least 6 guesses are neededto have 3 students with pencik.

b) probability to have the first student with pencil in at least 3 guesses.

guesses=try

Answer 1

Given the probability students have pencil is p= 0.40

a) Let X be the number of guesses needed to have r=3 students with pencil.

Therefore X follows negative binomial distribution.

The pmf of X is:

, for x=r,r+1,...

Therefore the probability that at least 6 guesses are needed to have 3 students with pencil is given by:

### By using Excel function:

P(X=3) by using function "=NEGBINOMDIST(3,3,0.4)"

P(X=4) by using function "=NEGBINOMDIST(4,3,0.4)"

P(X=5) by using function "=NEGBINOMDIST(5,3,0.4)"

Hence probability that at least 6 guesses are needed to have 3 students with pencil is

b) Let Y be the number of guesses needed to have first students with pencil.

Therefore Y follows geometric distribution.

The pmf of Y is:

; for x=1,2,3..

The probability to have the first student with pencil in at least 3 guesses given by:

The probability to have the first student with pencil in at least 3 guesses is