Question

A game has an expected value to you of ​$. It costs ​$ to​ play, but if you​ win, you receive​ $100,000 (including your ​$ ​bet) for a net gain of ​$. What is the probability of​ winning? Would you play this​ game? Discuss the factors that would influence your decision.

Answer 1

The probability of winning this game is 0.003

How to solve for the probability of winning

Let us name p to be the probability of winning the game.

We have the expected value to be 100

100 = probability of winning + 1-p x loss

win = 100000 - 200

We then input in the formula

100 = p*99800 +(1-p) x -200

100 = 99800p - 200 + 200p

Collect like terms

100 + 200 = 99800 + 200p

300 = 100000p

Divide through by 100000

This give the

Probability of winning =  0.003

The probability of winning the game is very low hence I would not play.

The factors that would influence the decision are:

• The cost of playing
• The expected value

Complete question

A game has an expected value to you of ?$100. It costs ?$200 to? play, but if you win you receive? $100,000 (including your ?$200 ?bet), for a net gain of ?$99,800. What is the probability of? winning

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