Suppose that someone offers you a bet concerning the tossing of a pair of fair dice. If both die turn up the same number, you will win $24. Otherwise you must pay $6 . Your expected winnings would be ________.
A.
$1.00
B.
$6.00
C.
-$1.00
D.
-$6.00
There are 6 possible doubles out of 36 possible combinations. So, on the average, you will roll a double once every 6 throws and you will win $24. But, again, on the average you will not throw a double 5 out of 6 throws and so will lose $30. Your average win, or rather loss, will be $24 - $30 = - $6 every 6 tosses or an average of - $6 / 6 = - $1 per toss.
Suppose that someone offers you a bet concerning the tossing of a pair of fair dice. If both die turn up the same number, you will win $24. Otherwise you must pay $6 . Your expected winnings would be ________.
A.
-$6.00
B.
$1.00
C.
$6.00
D.
-$1.00
To find the expected winnings, we need to calculate the probability of each outcome and then multiply it by the respective amount won or lost.
First, let's find the probabilities of the different outcomes:
1. The two dice show the same number: There are 6 possible outcomes where the dice show the same number (1-1, 2-2, 3-3, 4-4, 5-5, 6-6). Since each die has 6 possible outcomes, the probability is 6/36 = 1/6.
2. The two dice show different numbers: There are 30 possible outcomes where the dice show different numbers (6 possibilities for the first die and 5 possibilities for the second die, since we can't have the same number). So the probability is 30/36 = 5/6.
Now let's calculate the expected winnings:
The winnings when the two dice show the same number is $24, and the probability of this outcome is 1/6.
The winnings when the two dice show different numbers is -$6 (a loss of $6), and the probability of this outcome is 5/6.
Expected winnings = (Winning amount 1 * Probability 1) + (Winning amount 2 * Probability 2)
Expected winnings = ($24 * 1/6) + (-$6 * 5/6)
Expected winnings = $4 - $5
Expected winnings = -$1
Therefore, the expected winnings would be -$1.00.
The correct option is C. -$1.00.
Suppose that someone offers you a bet concerning the tossing of a pair of fair dice. If both die turn up the same number, you will win $24. Otherwise you must pay $6 . Your expected winnings would be ________.
A.
$1.00
B.
$6.00
C.
-$1.00
D.
-$6.00