1. A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on 1-hour flight is 0.02. What is the probability that

(a) Both will fail?

(b) Neither will fail?

(c) One or other will fail?

2. The contingency table below shows average yield (rows) and average duration (columns) for 38 bond funds.

For a randomly chosen fund, find the probability

(a) The bond fund is long duration.

(b) The bond fund has high yield.

(c) The bond fund has high yield given that it is of short duration.

(d) The bond fund is of short duration, given that has a high yield.

Solution Summary

The probability for various variables are determined.

The management of a bank in the Caribbean was concerned about the potential loss that might occur in the event of a hurricane. The bank estimated that the loss from one of these storms could be as much as $100 million including losses due to interrupted service and customer relations.
One project the bank is considering is

In a state that is going through financial difficulties, it is beleived that 5% of banks will fail. It is known that deposits of 90% of the banks in the state are insured by the FDIC. It is also believed that 3% of the banks insured by the FDIC will fail.
a) What is the probability that, for a randomly chosen bank, the bank

Q-7a. The management of a bank in the Caribbean was concerned about the potential loss that might occur in the event of a hurricane. The bank estimated that the loss from one of these storms could be as much as $100 million including losses due to interrupted service and customer relations. One project the bank is considering

A box contains glass lenses used for traffic signals. Six are red, four are yellow, and seven are green. If two are chosen at random find the probability they are both green, if:
a. the first lense is replaced before the second is chosen
b. the first lense is not replaced before the second is chosen.

A portable generator is needed at a remote construction site. Two alternatives are being considered. Their annual fixed costs and operating and maintenance costs per hour are shown in the table below. The contractor runs three 8-hour shifts per day for 250 working days per year
Generator 1
Fixed cost per year $4000
O&M

A fire detection sensor is tested for its failure rate and found to have a mean failure rate of 3.6E-2 per hour of exposure with a standard deviation of .4E-2 per hour. The distribution of the failure rates is normal. If a sensor is selected at random from a large lot for installation in a system, what is the probability that it

Stephanie Robbins is the Three Hills power Company management analyst assigned to simulate maintenance costs. In section 15.7 we describe the simulation of 15 generator breakdowns and the repair times required when one repairperson is on duty per shift. The total simulated maintenance cost of the current system is $4,320.
Robbi

A carton contains 12 eggs, five of which are cracked and seven of which are good. If four eggs are chosen at random, what is the probability that there will be three cracked and one good among the four chosen?

A grab bag contains 10 $1 prizes, 7 $5 prizes, and 5 $20 prizes. Three prizes are chosen at random. Find the following probabilities.
The probability that exactly two $20 prizes are chosen is
(Round to nearest thousandth as needed)
The probability that one of each prize is chosen is
(Round to nearest thousandth as need