You have 4 quarters and 2 dimes in your pocket. You draw two out at random. What is the expected value of the coins in cents that you draw

Answer 1

List all possible outcomes, calculate the probabilities. then calculated expected value.

Outcome Value Probability Value x Prob

2 quarters 50c 4C2*2C0 / 6C2 =6/15 20c

1 quarter, 1 dime 35c 4C1*2C1 / 6C2 = 8/15 18.6667c

2 dimes 20c 4C0*2C2/ 6C2 = 1/15 1.3333c

Sum= 40cents => Expected value

Note in the probability, these represents the # of ways of choosing those coins in the "outcome" from the set of all 6 coins:

The denominator is the # of ways of choosing 2 coins from the set of 6

The numerator is the # of ways of choosing the outcome -- e.g. # of ways of choosing 1 quarter and 1 dime is selecting 1 quarter from a set of 4 (4C1) multiplied by # of ways of choosing a dime from a set of 2 (2C1).