Question

A doughnut shop sells 5 different kinds of doughnut. a. how many distinct orders of 3 doughnuts are possible at this shop? b. assume all orders of 3 doughnuts are equally likely. Let x = the number of chocolate doughnut in an order. Find E(x).

Answer 1

A doughnut shop sells 5 different kinds of doughnut.

a) The number of distinct orders of 3 doughnuts are possible at this shop given by:

Therefore number of distinct orders are 10.

b) Assuming all orders of 3 doughnuts are equally likely.

Consider 5 doughnuts are A,B,C,D,E where C is a chocolate doughnut.

The possible orders are:{ABC,ABD,ABE,ACD,ACE,ADE,BCD,BCE,BDE,CDE}

Let x = the number of chocolate doughnut in an order.

The probability distribution of X is given by:

X=x P(X=x)

0 4/10

1 6/10

The expected value of X is given by:

E(X)= 0*(4/10)+1*(6/10)

E(X)=6/10

hence E(X)=6/10