1. Jane wins $21 if a die roll shows a six, and she loses $2 otherwise
Jane wins $21 if a die roll shows a six, and she loses $2 otherwise. Find the expected value (or expectation) of the game. Choose the answer from the following:
$1.83
$5.17
$9.50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Carol wins $10 if a die roll shows a six, and she wins $1 otherwise
Carol wins $10 if a die roll shows a six, and she wins $1 otherwise. Find the expected value (or expectation) of the game. Select the correct answer.
$2.50
$11.00
$1.83
$5.50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. A bag contains eight white balls and two black balls
A bag contains eight white balls and two black balls. John picks two balls at random from the bag, and he wins $6 if he does not pick a black ball. Find the expected value (or expectation) of the game. Select the correct answer.
$3.73
$2.27 $6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. A safe containing $1,000,000 is locked with a combination lock
A safe containing $1,000,000 is locked with a combination lock. You pay $3.5 for one guess at the six-digit combination. If you open the lock, you get to keep the million dollars. What is your expectation? Select the correct answer.
-$2.5
$2.5
$3.5 $4
-$4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. A bag contains 2 silver dollars and 6 slugs
A bag contains 2 silver dollars and 6 slugs. A game consists of reaching into the bag and drawing a coin, which you get to keep. Determine the “fair price” of playing this game. The “fair price” is the price at which the player can expect to break even if he plays the game many times, or in other words, the price at which his expectation is zero. Select the correct answer.
$0.25
$0.3
$0.125 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50