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  1. Home
  2. 12th grade
  3. Statistics & Probabilities
  4. Exercise : Determine the expected value for a game of chance

Determine the expected value for a game of chance Statistics & Probabilities

Paul flips a coin twice. If two heads come up, he wins $3. If two tails come up, he wins $2. Otherwise, he loses $2.

What is the expected value for this game of chance ?

There are 3 red marbles and 4 blue marbles in a bag. Richard is playing a game with his friend. If he picks a red marble out of the bag, then he gets $14. If he picks a blue marble, then he loses $7.

What is the expected value of this game?

Emma rolls a die. If she gets 6, then she wins $10. If she gets 1, then she loses $12. If she gets 2, 3, 4, or 5, then she wins $2, $3, $4 or $5 respectively.

What is the expected value for this game of chance ?

In a standard 52 deck, we randomly pick a card. If a face is drawn, then we win $3. If an ace is drawn, then we win $13. Otherwise, we lose $1.

What is the expected value for this game of chance?

In a game of chance, we roll two dice simultaneously. Let n be the sum of the numbers we get.

  • If n \ge 10, then we win $n.
  • If n \le 4, then we lose $n.
  • If 5 \le n \le 9, we don't win or lose anything.

What is the expected value for this game of chance ?

Louise and Paul are playing a game. Paul writes a number n from 0 to 9 on a piece of paper and asks Louise to guess the number. If she can guess the number correctly, then Paul will give her $10. Otherwise, she must give $2 to Paul.

What is the value of this game?

We flip a coin 3 times. For each heads up we win $2, and for each tail we lose $1.

What is the value of this game of chance?

See also
  • Course : Probability distributions
  • Exercise : Identify situations that fit the binomial distribution model
  • Exercise : Determine P(X=k) for a certain k and for X following a given binomial distribution, using the formula
  • Exercise : Determine P(-k≤X≤k) when X follows the standard normal distribution
  • Exercise : Determine P(a≤X≤b) when X follows any normal distribution and a and b are given
  • Exercise : Determine a such that P(-a≤X≤a)=b, when X follows the standard normal distribution and b is given
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