You bought one $2 chance on an $84 radio. Sixty chances were sold. What is your expectation?

To calculate your expectation in this scenario, you need to consider the probability of winning and losing, as well as the corresponding outcomes.

First, let's calculate the probability of winning. You purchased one chance out of sixty, so your probability of winning is 1/60.

Next, let's determine the amount you would win or lose. The cost of the radio is $84, and you only paid $2 for your chance. If you win, you would save $84, as you would receive the radio without paying the retail price. If you lose, you would lose the $2 you paid for the chance.

Now, let's calculate the expectation by multiplying the probability with its corresponding outcome.

Expected Value = (Probability of Winning * Amount Won) + (Probability of Losing * Amount Lost)

Expected Value = (1/60 * $84) + (59/60 * -$2)

Expected Value = $1.40 - $1.97

Expected Value = -$0.57

Therefore, your expectation in this scenario is -$0.57, indicating that over the long run, you can expect to lose an average of $0.57 for every $2 chance you purchase.