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:$7.8

Step-by-step 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.