Suppose there are 15 different color crayons in a box. each time one obtains a crayon, it is equally likely to be any of the 15 types. compute the expected # of different colors that are obtained in a set of 5 crayons. (hint: use indicator variables and linearity of expectation)

4.38

Step-by-step explanation:

There 15 different color crayon in a box.

We will enumerate the crayon from 1 to 15

Let Xi be the indicator random variable for the event that the ith crayon is among the set of 5 crayon.

E[Xi] = Pr(at least one type i crayon is in the set of 5)

E[Xi] = 1 - Pr(no type i crayons are in the set of 5)

= 1 - (14/15)^5

The expected number of crayon is

E(summation of Xi for the 15 crayons where i = 1) = 25(1- (14/15)^5)

= 4.38

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.