Question

Debra is buying prizes for a game at her school's fundraiser. The game has three levels of prizes, and she has already bought the second and third prizes. She wants the first prize to be nice enough to attract people to the game. The game's manufacturer has supplied her with the probabilities of winning first, second, and third prizes. Tickets cost $3 each, and she wants the school to profit an average of $1 per ticket. How much should she spend on each first prize

Answer 1

Answer:

$9.19

Step-by-step explanation:

We are given that

Cost of each ticket=$3

Average profit per ticket=$1

Expect gain for ticket purchaser must be -$1

Let x be the cost of first prize

Probability of first prize=0.15

Probability of second prize=0.30

Probability of third prize=0.45

Cost of second prize=$1.15

Cost of third prize=$0.74

Total probability=0.15+0.30+0.45=0.9

Probability of winning =0.9

Probability of losing=1-0.9=0.1

According to question

$x(0.15)+0.30(1.15)+0.74(0.45)-3(0.1)=-1$

$0.15x+0.378=-1$

$0.15x=-1-0.378$

$0.15x=-1.378$

$x=-\frac{1.378}{0.15}=-9.19$

Hence, she spend money on each first prize=$9.19