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What is the expected value to you of the following game: You and another person have 3 coins each. You both flip all of your coins and if your three coins show the same number of tails as the other person, you pay them $2, otherwise they pay you $1.

4 Answers


Here's the explanation to the above (Since none was given): There are four different number of Tails that can be shown when you flip 3 coins: 0,1,2,3. The Probability of 0 Tails, P(0T) = 1/16, P(3T) = 1/16, P(1T) = 3/16, P(2T)=3/16. Since your flips and your opponent's flips are independent, we know that the Probability that I roll 0 tails and you roll 0 tails = P(0T)*P(0T). Thus, square each of the above probabilities and sum them: you get 1/64+1/64+9/64+9/64=20/64. Thus P(same number of Tails) = 20/64 = 5/16. Now it is asking you for expected value, so plug the above probability into an expected value equation: (5/16)(-2) + (11/16)(1) = 1/16 ie, 5/16 of the time you roll the same number of tails and lose two dollars, 11/16 of the time you don't and you win a dollar, thus your expected value of each play of the game is 1/16 of a dollar. (In the long run if you play many times you should expect to win that much per play)

The above has the correct answer, but the probabilities are 1/8, 1/8, 3/8, 3/8. Then square them....and so on.

What is 29^2?

4 Answers

If you have a deck of cards split into 4 piles and was offered 1:1 odds to draw a face card (J Q K A) from at least one of the piles, would you take the game? Why or why not?

4 Answers

What the probability of getting 2 consecutive heads in a total of N tosses (I found this one pretty hard and I didn't figure out the right answer at the time.)

4 Answers

Roll a fair dice, if it's a prime number, you pay me that number times $100, if it's not a prime number, I pay you that number times $100. Consider 1 as a prime number. How much willing to pay to play this game.

7 Answers

How many degrees separate the hands on an analog clock at 3:15?

3 Answers

What are odds of getting EXACTLY two (2) heads if you flip a fair coin 10 times?

2 Answers

What angle does that clock make at 4:15? If you have 100 red and white marbles and had to place them in two separate jars - how would you distribute the marbles to give you the highest chance (EV) of getting a red marble when you are blindfolded? You have to use all the marbles.

1 Answer

Why are you here? What makes you think you can do this job and aren't just wasting my time?

1 Answer

You have a cube made of 10x10x10 smaller cubes. You paint the faces and break the whole cube. How many smaller cubes have at least one painted face?

1 Answer
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