You have a $9000 motorcycle and a $850 bicycle. The probability that your motorcycle will be stolen next year is .02, but the probability that your bike will be snatched is .1. The insurance company offers you theft protection for your motorcycle for $200 and theft protection for your bicycle for $75. What is the expected value of the motorcycle protection? What is the expected value of the bicycle protection?

expected value of motorcycle protection = .02(9000) = 180

expected value of bike protection = .1(850) = 85

To calculate the expected value of the motorcycle protection, we need to consider the value of the protection and the probability of the motorcycle being stolen.

The value of the protection is $200, and the probability of the motorcycle being stolen is 0.02.

Expected value = Value of protection * Probability of theft
Expected value = $200 * 0.02
Expected value = $4

Therefore, the expected value of the motorcycle protection is $4.

Now let's calculate the expected value of the bicycle protection.

The value of the bicycle protection is $75, and the probability of the bike being stolen is 0.1.

Expected value = Value of protection * Probability of theft
Expected value = $75 * 0.1
Expected value = $7.50

Therefore, the expected value of the bicycle protection is $7.50.