) Laura McCarthy, the owner of Riverside Bakery, has been approached by insurance underwriters trying to convince her to purchase flood insurance. According to local meteorologists, there is a 0.01 probability that the river will flood next year. Riverside’s profits for the coming year depend on whether Laura buys the flood insurance and whether the river floods. The profits (which take into consideration the $10,000 premium for the flood insurance) for the four possible combinations of Laura’s choice and river conditions are:

The River
Does Not
Flood Floods
Insurance No Flood
Decision Insurance $200,000 -$1,000,000
Get Flood
Insurance $190,000 $200,000
a. If Laura decides not to purchase flood insurance, use the appropriate discrete probability distribution to determine Riverside’s expected profit next year.
b. If Laura purchase the flood insurance, what will be Riverside’s expected profit next year?
c. Given the results in parts (a) and (b), provide Laura with a recommendation.

a. To determine Riverside's expected profit next year if Laura decides not to purchase flood insurance, we need to calculate the weighted average of the profits for each possible outcome, considering the probability of each outcome occurring.

The profits and their corresponding probabilities are as follows:
- If the river does not flood and Laura does not purchase insurance: $200,000 with a probability of (1 - 0.01) = 0.99
- If the river floods and Laura does not purchase insurance: -$1,000,000 with a probability of 0.01

To calculate the expected profit, we can multiply each profit by its corresponding probability and sum the results:

Expected profit = ($200,000 * 0.99) + (-$1,000,000 * 0.01)

b. To determine Riverside's expected profit next year if Laura purchases flood insurance, we follow the same process as in part (a) but with different probabilities.

The profits and their corresponding probabilities are as follows:
- If the river does not flood and Laura purchases insurance: $190,000 with a probability of (1 - 0.01) = 0.99
- If the river floods and Laura purchases insurance: $200,000 with a probability of 0.01

Expected profit = ($190,000 * 0.99) + ($200,000 * 0.01)

c. To provide a recommendation to Laura, we compare the expected profits from part (a) and part (b). If the expected profit with flood insurance is higher, it would be recommended for Laura to purchase the flood insurance. Otherwise, it would be recommended for her not to purchase it.

The four possibilities are:

Buy, flood
Buy, no flood
Don't buy, flood
Don't buy, no flood

However, since there are no estimates of the profits from the previous year, more data is needed to estimate the profits under those conditions.

I hope this helps. Thanks for asking.