21.9% is 7 million as a percentage of 32 million
To find the percent of error divide how off the wrong answer was by the right number, then multiply by 100.
Bryan's guess of 730 was 120 less than the actual number so you would divide 120 by 850. 120/850 = 0.141
Then we would multiply that by 100. 0.141 * 100 = 14.1
His percent of error was 14.1%. The percent of error is negative since his guess was less than the right answer.
Answer: 2.77
The expected value is positive, so you expect to gain on average $2.77 per draw.
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Explanation:
Define two events
W = winning = getting a card 4 or less
L = losing = getting 5 or higher
P(W) = probability of winning
P(W) = 12/52 since there are 12 cards that are four or less out of 52
P(W) = 3/13 for any suit of 13, there are 3 cards that are four or less
P(L) = 1-P(W)
P(L) = 1-3/13
P(L) = 13/13 - 3/13
P(L) = 10/13
V(W) = net value of winning
V(W) = 162
V(L) = net value of losing
V(L) = -45
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E(X) = expected value
E(X) = P(W)*V(W) + P(L)*V(L)
E(X) = (3/13)*162 + (10/13)*(-45)
E(X) = 36/13
E(X) = 2.76923076923077
E(X) = 2.77 rounding to two decimal places (to the nearest cent)
This game is in favor to the player since we got a positive expected value. A fair game would occur if the expected value was 0.
