Final answer:
To find the expected value of the total value of two coins taken at random from a bag, calculate the weighted average of all possible outcomes by multiplying each outcome's value by its probability and summing these products.
Step-by-step explanation:
To find the expected value, E(X), of the total value of two coins taken at random without replacement from a bag containing 8 nickels (each worth $0.05), 2 dimes (each worth $0.10), and 6 quarters (each worth $0.25), we need to calculate the weighted average of all possible outcomes, taking into account their probabilities.
First, we should list out all possible outcomes and their corresponding probabilities. Then, each outcome's total value is multiplied by its probability, and all these products are then summed to obtain E(X).
Calculating all possibilities by hand can be extensive, so typically you would use combinatorics to find out the number of ways picking different combinations of coins and their associated probabilities. After finding that, you would use the formula E(X) = μ = Σ xP(x) to compute the expected value by multiplying the value of outcomes by their probabilities and summing them up.