A pool of 10 policies has 2 policies from region A, 5 policies from region B, and 3 policies from region C. What is the probability that one policy from region A is selected, two policies from region B are selected, and 2 policies from region C are selected?

• 0.2
• 0.212
• 0.22
• 0.225
• 0.235

An insurance agent meets twelve potential customers independently, each of whom is equally likely to purchase an insurance product. Six are interested only in auto insurance, four are interested only in homeowners insurance, and two are interested only in life insurance. The agent makes six sales.

Calculate the probability that two are for auto insurance, two are for homeowners insurance, and two are for life insurance.

• 0.001
• 0.024
• 0.069
• 0.097
• 0.500

Six claims are to be randomly selected from a group of thirteen different claims, which includes two workers compensation claims, four homeowners claims and seven auto claims.

Calculate the probability that the six claims selected will include one workers compensation claim, two homeowners claims and three auto claims.

• 0.025
• 0.107
• 0.153
• 0.245
• 0.643

A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems in inventory from Source A, 20% are defective. Of the modems in inventory from Source B, 8% are defective.

Calculate the probability that exactly two out of a sample of five modems selected without replacement from the store’s inventory are defective.

• 0.010
• 0.078
• 0.102
• 0.105
• 0.125

Two fair dice are rolled. Let [math]X[/math] be the absolute value of the difference between the two numbers on the dice. Calculate the probability that [math]X\lt 3 [/math].

• 2/9
• 1/3
• 4/9
• 5/9
• 2/3

In a group of 25 factory workers, 20 are low-risk and five are high-risk. Two of the 25 factory workers are randomly selected without replacement. Calculate the probability that exactly one of the two selected factory workers is low-risk.

• 0.160
• 0.167
• 0.320
• 0.333
• 0.633

Five people get on an elevator that stops at five floors. Assuming that each has an equal probability of going to any one floor, find the probability that they all get off at different floors.

• 0.0332
• 0.035
• 0.0384
• 0.04
• 0.0434

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Determine the probability that among a set of 5 people, at least two have their birthdays in the same month of the year (assuming the months are equally likely for birthdays).

• 0.58
• 0.62
• 0.65
• 0.68
• 0.72

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Two fair dice are tossed. One die is red and one die is green.

Calculate the probability that the sum of the numbers on the two dice is an odd number given that the number that shows on the red die is larger than the number that shows on the green die.

• 1/4
• 5/12
• 3/7
• 1/2
• 3/5

In a shipment of 20 packages, 7 packages are damaged. The packages are randomly inspected, one at a time, without replacement, until the fourth damaged package is discovered.

Calculate the probability that exactly 12 packages are inspected.

• 0.079
• 0.119
• 0.237
• 0.243
• 0.358