A convenience store has made up 20 grab bag gifts and is offering them for $3 a bag. 9 bags contain merchandise worth 50 cents. Eights bags contain merchandise $2.25, and three bags contain merchandise worth $5. Suppose you purchase one bag, what is your expected gain or loss?

Probability of selecting a bag contain merchandise worth 50 cents is 9/20 = 0.45

Probability of selecting a bag contain merchandise worth $2.25 is 8/20 = 0.4

Probability of selecting a bag contain merchandise worth $5 is 3/20 = 0.15

Expected gain/loss = 0.45*9 + 0.4*8 + 0.15*3 - 3 = 4.05+3.2+0.45 - 3 = 4.7

Hence there is expected gain of 4.7

Expected loss = $-1.13

Step-by-step explanation:

9 bags contain merchandise worth $0.50

8 bags contain merchandise worth $2.25

3 bags contain merchandise worth $5

Total bags are 20

$0.50 * (9/20) + $2.25 * (8/20) + $5 * (3/20)

$0.225 + $0.9 + $0.75

$1.87

The cost of bag is $3

The expected value is

E = $1.87 - $3

E = $-1.13 (this is a loss)

So you are most likely to lose $1.13 if you purchase 1 bag at the convenience store.