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In a​ state's pick 3 lottery​ game, you pay ​$1.33 to select a sequence of three digits​ (from 0 to​ 9), such as 288. if you select the same sequence of three digits that are​ drawn, you win and collect ​$384.13.

Respuesta :

A. How many different selections are possible?

B. What is the probability of winning?

C. If you win, what is your net profit?

D. Find the expected value

Answer :

A. sequence of three digits​ (from 0 to​ 9). so 10 numbers.

We know 3 lottery games. So possible selections = 10^3 = 1000

B. Probability of winning = one outcome / total outcomes

P( winning) = [tex] \frac{1}{1000} [/tex] = 0.001

c. Net profit = winning amount - paid amount

= 384.13 - 1.33 = $382.8

D. expected value

E(x) = net profit * winning probability - paid amount * lost probability

E(x) = 382.8 * 0.001 - 1.33 * 0.999 = -0.95

you expect to lose 95 cents per ticket.

fichoh

The expected value, sample size and net winning of the experiment in question is given below :

  • Number of possible selections = 1000
  • Probability of winning = 0.001
  • Net winning = $382.80
  • Expected value = - 0.945

The number of values that can be selected = (0 - 9) = 10 values

The number of possible selections

  • [tex]10^{n} [/tex] ; n = Number of values to be selected

Number of ’possible selections = [tex]10^{3} = 1000[/tex]

The probability of winning :

  • Number of winnings / Number of possible selections

Number of winnings = 1

Probability of winning = 1 / 1000 = 0.001

The net winning :

Winning amount - amount paid

$384.13 - $1.33 = $382.80

The Expected value :

(Net winning × winning probability) - (Amount paid × probability of not winning)

(382.80 × 0.001) - (1.33 × (1 - 0.001))

0.3282 - 1.32867 = - 0.945

Learn more : https://brainly.com/question/18405415

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