You get to throw a die. If you roll a 3, you win $6. If you roll a 1 or a 5, you
win $3. If you roll an even number, you lose $6. Find your expectation for this
game.
Two Fair Dice are thrown and the differance is noted.Draw the sample space.What is the probability that ther is no differance.
To find the expectation for this game, we need to calculate the expected value for each possible outcome and then add them up.
The possible outcomes are:
- Rolling a 3: Probability = 1/6; Winning amount = $6
- Rolling a 1 or 5: Probability = 2/6; Winning amount = $3
- Rolling an even number: Probability = 3/6; Losing amount = -$6
To calculate the expected value, we multiply the probability of each outcome by the amount won (or lost), and then sum them up:
Expected value = (1/6 * $6) + (2/6 * $3) + (3/6 * -$6)
Simplifying the equation:
Expected value = $1 + $1 - $3
Expected value = -$1
So, the expectation for this game is -$1. On average, you can expect to lose $1 per game.