A game consists of tossing two coins, first a dime and then a nickel. For each coin which comes up a head you win the value of the coin. For each coin which comes up a tail you get nothing.

Question

{HH,HT,TH,TT} - each outcome with probability .25 - winnings are 15,10,5,0

a) Find the mean or expected winnings

b) Find the standard deviation of your winnings.

c) If you had to pay a dime to play the game, what would be the mean of your winnings?

d) If you had to pay a dime to play the game, what would be the standard deviation of your winnings?

Answer 1

Expected winning can be found by summing over all possible outcomes the product of winning and the respective probability.

For outcome HH:
winning=0.25
probability = 0.25
prodcut = 0.25*0.25=0.0625

Repeat for the 3 other outcomes, and add the 4 products together to get the expected winning.

Answer 2

The breaking strength (in pounds) of a certain new synthetic is normally distributed, with a mean of 170 and a variance of 4. The material is considered defective if the breaking strength is less than 166 pounds. What is the probability that a single, randomly selected piece of material will be defective?