Roulette is a casino game that involves players betting on where a ball will land on a spinning wheel. An American roulette wheel has 38 numbered slots — half of the slots from 1 to 36 are red and the other half are black. Slots 0 and 00 are both green.

Suppose that a player bets $1 on the color red. If the ball lands in a red slot, the player gets their initial $1 back plus a payout of $1. If the ball doesn't land in a red slot, they lose their $1 bet. Let X= the player's net gain from a $1 bet on a the color red. Here is the probability distribution of X:

Win Lose

X=net gain $1 -$1

P(X) 18/38 20/38

Calculate the mean of X

You may round your answer to the nearest thousandth.

Question

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Respuesta :

ridamsworld ridamsworld · Answer 1 · 2021-04-08T10:56:19+02:00

Answer: -0.053

Step-by-step explanation:

1•(18/38) + -1 •(20/18) = -0.053

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joaobezerra joaobezerra · Answer 2 · 2021-12-03T13:10:10+01:00

Using the discrete distribution, the mean of X is of -0.053.

The expected value of a discrete distribution is the sum of each outcome multiplied by it's respective probability.

In this problem, the distribution is:

[tex]P(X = 1) = \frac{18}{38}[/tex]

[tex]P(X = -1) = \frac{20}{38}[/tex]

Hence:

[tex]E(X) = \frac{18}{38} - \frac{20}{38} = -\frac{2}{38} = -0.053[/tex]

The mean of X is of -0.053.

A similar problem is given at https://brainly.com/question/24855677