Your friend tosses 3 coins and you roll a single die. If the number on the die you roll is less than or equal to the number of heads that your friend tosses, you win $X. If not, you lose $1. How large should X be in order for this to be a fair game?
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

Htt tHt ttH
HHt tHH HtH
HHH
ttt
Each of these probabilities is 1/8
Now multiple each by the probability of getting the die equal or less..
example:
HHt*2/6=2/48
HtH=2/48
and so on Add all the cases, and add the probabilities. That is the probability of winning.
Expected value= Probability of winning*X(1Prwinnig)1
So you have to calculate X so that the expected value is =0 for a fair game. 👍
 👎
 ℹ️
 🚩
👤bobpursley
Answer this Question
Related Questions

Algebra
Your friend claims that she has a bag of 30 coins containing nickels, dimes, and quarters. The total value of the 30 coins is $3. There are twice as many nickels as there are dimes. Is your friend correct? Explain your reasoning

probability
Consider 10 independent tosses of a biased coin with the probability of Heads at each toss equal to p, where 0

physics
For a flourish at the end of her act, a juggler tosses a single ball high in the air. She catches the ball 3.6 s later at the same height from which it was thrown. Part AWhat was the initial upward speed of the ball?2sf

Statistics
As in the previous lecture clip, consider the same example of two rolls of a 4sided die, with all 16 outcomes equally likely. As before, let X be the result of the first roll and Y be the result of the second roll. Define W=XY . Find the numerical values

probability
We have two fair threesided dice, indexed by i=1,2. Each die has sides labelled 1, 2, and 3. We roll the two dice independently, one roll for each die. For i=1,2, let the random variable Xi represent the result of the ith die, so that Xi is uniformly

Math
You roll a fair sixsided die (all 6 of the possible results of a die roll are equally likely) 5 times, independently. Let X be the number of times that the roll results in 2 or 3. Find the numerical values of the following. a) pX(2.5)= b) pX(1)=

Statistics
you roll two fair dice, a green one and a red one? (a) are the outcomes on the dice independent? (b)Find P(1 on green die and 2 on red die) (c)Find P(2 on green die and 1 on red die) (d)Find P(1 on green die and 2 on red die) or (2 on green die and 1 on

Probability
The newest invention of the 6.041x staff is a threesided die. On any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4. Consider a sequence of six independent rolls of this die. 1. Find the

Math
All students in Peter's class have $1.05, consisting of nickels and/or dimes and/or quarters. Each student has a different combination of coins, and all possible combinations of coins are included. What is the probability that Peter is unable to give his

MATH!
An experiment consists of rolling a weighted die. The probability of rolling each number is: Pr[1]=0.05, Pr[2]=0.1, Pr[3]=0.25, Pr[4]=0.25, Pr[5]=0.2, and Pr[6]=0.15. On the first roll, you record if the number is Small (1,2) or Large (3,4,5,6). If the

Probability
We have two coins, A and B. For each toss of coin A, we obtain Heads with probability 1/2; for each toss of coin B, we obtain Heads with probability 1/3. All tosses of the same coin are independent. We select a coin at random, where the probabilty of

Math
theoretically if you roll a number cube 36 times, how many times would you expect to roll the number one? could you also give me explanation? Thank you. and also answer as fast as possible.

Math
Two dice are rolled. Find the probability that an even number is rolled on one die and an odd number is rolled on the second die.

Math
We are interested in calculating the probability that there are 5 Heads in the first 6 tosses and 3 Heads in the last 5 tosses. Give the exact numerical values of a , b , c , d that would match the answer ap7(1−p)3+bpc(1−p)d.

science
In the diagram above, the arrows represent momentum. A larger arrow indicates more momentum. Which of the following best describes how the balls will move after ball A collides with ball B? (1 point) 1. Ball A will bounce off of ball B and roll to the

math
On a single roll of a pair of dice, what are the odds against rolling a sum of 7? Please help immediately! :(

math
consider the equation x^2+kx+1=0 a single fair die(dice)is rolled to determine the value of the middle coefficient, k. the value for k is the number of dots on the upper face of the die. what is the probability that the equation will have real, unequal

math
Suppose you are going to roll a die 60 times and record the proportion of times that a 1 or 2 is showing, s. The sampling distribution of s should be centered about....?

Probability
The newest invention is a threesided die. On any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4. Consider a sequence of six independent rolls of this die. 1. Find the probability that exactly two

Probability
You roll two fivesided dice. The sides of each die are numbered from 1 to 5. The dice are “fair" (all sides are equally likely), and the two die rolls are independent. Part (a): Event A is “the total is 10" (i.e., the sum of the results of the two die
Still need help?
You can ask a new question or browse existing questions.