Jon P. answered • 04/20/15
Tutor
5.0
(173)
Harvard honors math degree, experienced tutor in math and ACT prep
To calculate expected value multiply the probability of each outcome by its value, and add them up:
Quarter: Probability = 3/12 = 1/4, value = 25¢. 1/4 * 25 = 6.25
Dime: Probability = 5/12, value = 10¢. 5/12 * 10 = 4.17
Nickel: Probability = 4/12 = 1/3, value = 5¢. 1/3 * 5 = 1.67
Total: 6.25 + 4.17 + 1.67 = 12.09 ¢
Jon P.
tutor
That's an interesting question. With two coins, there are nine possible outcomes: QQ (quarter on the first pick, quarter on the second pick), QD, QN, DQ, DD, DN, NQ, ND, and NN. Each has a specific probability, and each has a specific value. E.g., the probability of getting a quarter on the first pick is 3/12 (=1/4). And if a quarter is chosen the probability of getting another quarter is 2/11 (11 coins left, of which two are quarters). So the probability of QQ is (1/4)(2/11) = 2/44 = 1/22. The value of QQ is $.25 + $.25 = $0.50. So the contribution of this possible outcome to the total expected value is 1/22 x $0.50. Each of the nine outcomes can be analyzed this way to determine its probability and its value, and from that we can calculate the expected value in the same way as always -- i.e., the sum of the all the products of probability times value.
That being said, there may be a simpler way to do the math, using formulas from combinatorics. However, thinking about the problem in terms of the nine possible outcomes, as I described it above, gives the clearest view of the underlying idea of how one goes about analyzing an expected value problem and applying it to this situation.
Report
10/10/19
Kaylie J.
What if you are selecting two coins?10/09/19