Question

A bowl contains 10 chips, of which 8 are marked $2 each and 2 are marked $5 each. Let a person choose, at random and without replacement, three chips from this bowl. If the person is to receive the sum of the resulting amounts, find his expectation.

Answer 1

Answer:$7.8

Explanation:

We have three cases to this question which are;

(a). Getting two $2 and one $5

(b). Getting one $2 and two $5

(c). Getting all three $2

Note: there are 10:3 ways of doing this.

Computing the probability of each, we have:

(a). We have {8;2} {2;1} ways to get two $2. Therefore, the probability gives;

(8;2) (2;1)÷ 10;3) we get 9 here.

(b). (8;1)(2;2)÷ (10;3)

We have 12 here.

(c). (8;3)(2;0)÷ (10;3)= 6

The expectation;

(10;3)= 120, (8;3)(2;0)= 56.

(8;2)(2;1)= 56 and (8;1)(2;2)= 8.

So, the expectation is;

9.56+12.8+6.56÷120

= 936÷120

= 39÷5

= $7.8.