The Big River Casino is advertising a new digital lottery-style game called Instant Lotto. The player can win the following mone

Answer:

(a) For a single play of Instant Lotto, the anticipated value of the prize amounts to $3.50.

(b) The likelihood that a visitor secures a prize at least two times during the 20 free plays is 0.2641.

(c) The chance of a randomly chosen day having 1000 or more players of Instant Lotto is 0.2579.

Step-by-step explanation:

(a)

The probability distribution for the monetary awards in Instant Lotto is defined as follows:

X P (X = x)

$10    0.05

$15    0.04

$30    0.03

$50    0.01

$1000  0.001

$0      0.869

___________

Total =   1.000

The expected value for one Instant Lotto play can be computed as follows:

Consequently, the expected prize value for a single Instant Lotto play is $3.50.

(b)

Define X as the count of prizes a visitor wins.

A visitor receives n = 20 complimentary plays of Instant Lotto.

The probability of winning in any of the 20 games is p = 1/20 = 0.05.

The outcomes in the 20 plays are independent of one another.

The variable X adheres to a Binomial distribution characterized by parameters n = 20 and p = 0.05.

To find the probability that the visitor wins a prize at least twice in these 20 plays, perform the following calculation:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

The resulting probability that the visitor wins a prize at least twice during the 20 plays is 0.2641.

(c)

Let X denote the number of individuals playing Instant Lotto each day.

The variable X is assumed to be normally distributed with a mean value of μ = 800 players and a standard deviation of σ = 310 players.

To ascertain the probability that on a random day, at least 1000 people participate in Instant Lotto, consider the following:

Implementing continuity correction:

P (X ≥ 1000) = P (X > 1000 + 0.50)

                    = P (X > 1000.50)

The probability of having at least 1000 players on any random day is 0.2579.