f a $2 bet is placed for a chance to win $500 for drawing a 10 of any suit from a standard deck of
cards, what is the value of expectation?
A. $125
B. $250
C. $500
D. $2
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well, P(success) = 1/13
so use that as usual
To find the value of expectation, we need to multiply the probability of each outcome by its associated value and then sum those values.
In this case, there is a total of 4 tens in a standard deck of cards (one for each suit - hearts, diamonds, clubs, and spades). Since you have to draw a 10 of any suit, there are 4 favorable outcomes out of 52 possible outcomes.
Thus, the probability of winning is 4/52, which simplifies to 1/13.
The value associated with winning is $500, and the value associated with losing is -$2 (the cost of the bet).
Now, let's calculate the expectation:
E(X) = (value of winning * probability of winning) + (value of losing * probability of losing)
= ($500 * 1/13) + (-$2 * 12/13)
= ($500/13) - ($24/13)
= $476/13
So, the value of expectation is approximately $36.62.
However, since the available answer choices are in whole dollars, we need to round the value of expectation to the nearest whole dollar. In this case, the rounded value is $37.
Therefore, the value of expectation is not one of the given answer choices (A, B, C, or D).