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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Games of Chance If x is a player’s net gain in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose over the long run. In Exercises 35 and 36, find the player’s expected net gain for one play of the specified game.

Roulette In roulette, the wheel has the 38 numbers 00, 0, 1,2,…, 34, 35, and 36, marked on equally spaced slots. If a player bets $1 on a number and wins, then the player keeps the dollar and receives an additional $35. Otherwise, the dollar is lost.

To determine

To calculate: The expected net gain for one play of the specified game of the wheel which has 38 numbers as 00,1,2,3,,37,38.

Explanation

Given Information:

The wheel has 38 numbers 00,1,2,3,,37,38. In the game if the Player bets $1 on a number and

wins then the player will receive an additional of $35 over $1 and if he loses the bet then the

dollar is lost.

Formula used:

In a set m {x1,x2,xm} where x1,x2... are the values of discrete random variable in which the probability of occurring of these values in the provided set are p(x1),p(x2),p(xm).

The expected value of the random variable is;

E(x)=x1p(x1)+x2p(x2)++xmp(xm)

Calculation:

Consider the above expected value formula in which xm represents the amount player will have after winning or losing a bet

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