Question

In a​ state's Pick 3 lottery​ game, you pay $1.47 to select a sequence of three digits​ (from 0 to​ 9), such as 700.

If you select the same sequence of three digits that are​ drawn, you win and collect $380.47.

Complete parts​ (a) through​ (e).

a. How many different selections are​ possible?

b. What is the probability of​ winning? ​(Type an integer or a​ decimal.)

c. If you​ win, what is your net​ profit? (Type an integer or a​ decimal.)

d. Find the expected value. (Round to the nearest hundredth as​ needed.)

e. If you bet $1.47 in a certain​ state's Pick 4​ game, the expected value is negative $1.09.

Which bet is​ better, a $1.47 bet in the Pick 3 game or a $1.47 bet in the Pick 4​ game? Explain.

A.

The Pick 4 game is a better bet because it has a larger expected value.

B.

The Pick 3 game is a better bet because it has a larger expected value.

C.

Neither bet is better because both games have the same expected value.

Answer 1

a.

No. of different selections that are​ possible =1000

(001, 002, 003,......., 1000)

(OR)

Available digits from 0 to 9 is n =10

No. of digits required to select is r =3

Repetition: Allowed

So, No. of different selections possible =n^r =10³ =1000

b.

Let the probability =P

P(winning) =1/1000 =0.001

c.

Net profit on winning =380.47 - 1.47 =$379.00

d.

Expected value =winning amount*P(winning) + losing amount*P(losing) =379(0.001) + (-1.47)(0.999) =0.379 - 1.46853 = -1.09

e.

Option C. is correct.

"Neither bet is better because both games have the same expected value of negative $1.09 which means in the long run you are expected to lose $1.09".