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?

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:

Step 3

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

Tagged in

Q: Let S = {0, 1, 2, 3, 4, 5, 6, 7, 8} be a uniform sample space, and determine the probability that a ...

A: Solution:Concept of probability:Probability deals with the likelihood of occurrence of a given event...

Q: Question # 4 Consider a circular table with N > 4 seats. Chris and Sarah are two of N th at ests to ...

A: Given a circular table with N seats (N ≥4). Chris and Sarah are two among the N dinner guests,Let us...

Q: A diagnostic test for disease X correctly identifies the disease 90% of the time. False positives oc...

A: Given probability that test detects disease X correctly = 0.90probability that false positive = 0.0...

Q: 2.5. Let N be a random variable with distribution function 0 if <0 F(2) = 〈a,2 if 0 < x < 1 Find P{1...

A: Given cumulative ditribution function F(x) as shown belowTo find the P(1/4 < X< 5) According t...

Q: Two fair dice are rolled at once. Find the conditional probability that the sum is 6, given that the...

A: Concept of conditional probability:For any two events A and B with P(B) >0, the formula for condi...

Q: Think about a density curve that consists oftwo straight-line segments. The first goes fromthe point...

A: Hello there! there are more than 3 subparts in this question. I cannot answer more than 3 subparts p...

Q: A poll asked the question, "What do you think is the most important problem facing this country toda...

A: The percentage of responndents answered crime and violence = 25%95% confidence interval margin of e...

Q: A density curve consists of the line segment connecting the points (0,1) and (0.5,1) and the segment...

A: Hello there!There are more than 3 subparts mentioned in the question. I can answer only 3 subparts i...

Q: At local industry, the scheduler is facing adilemma. A shaft must go through the following threediff...

A: Given that there are 4 centering machines and only 2 needed There are 3 grinding machines and only 1...

Sorry about that. What wasn’t helpful?