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You play the following game: You bet $1, a fair die is rolled and if it shows 6 you win $4, otherwise you lose your dollar. If you must choose the number of rounds in advance, how should you choose it to maximize your chance of being ahead (having won more than you have lost) when you quit, and what is the probability of this?

Question

You play the following game: You bet $1, a fair die is rolled and if it shows 6 you win $4, otherwise you lose your dollar. If you must choose the number of rounds in advance, how should you choose it to maximize your chance of being ahead (having won more than you have lost) when you quit, and what is the probability of this?

check_circleAnswer
Step 1

you roll a 6, 1/6 of the time you get $4.

you roll a 5, 1/6 of the timeyou loose $1.

you roll a 4, 1/6 of the time you loose $1.

you roll a 3, 1/6 of the time you loose $1.

you roll a 2, 1/6 of the time you loose $1.

you roll a 1, 1/6 of the time you loose $1.

Step 2

Now we will find the expected value  of the game as follows: 

 

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Step 3

As the expected value of the game in a negative value. ...

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Probability

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