Red and blue balls are placed in two urns. One urn contains 5 red balls and 8 blue balls and the other urn contains 6 red balls and 4 blue balls. Two balls are randomly selected from each urn.

Determine the probability that two balls of differing colors are observed.

• 0.9094
• 0.9154
• 0.92
• 0.952
• 0.9527
• 0.9627

An insurance company employs 10 claims adjusters at a local office where 4 adjusters deal with home insurance claims, 2 adjusters deal with auto insurance claims, and 4 adjusters deal with travel insurance claims. The local office receives 6 new reported claims from policyholders: 2 claims for auto, 3 claims for home, and 1 claim for travel.

If each reported claim is allocated to an adjuster in a random manner, determine the probability that all reported claims will be serviced by an adjuster that is qualified to service the claim.

• 0.05
• 0.0545
• 0.0622
• 0.0682
• 0.0762

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 urn contains four fair dice. Two have faces numbered 1, 2, 3, 4, 5, and 6; one has faces numbered 2, 2, 4, 4, 6, and 6; and one has all six faces numbered 6. One of the dice is randomly selected from the urn and rolled. The same die is rolled a second time. Calculate the probability that a 6 is rolled both times.

• 0.174
• 0.250
• 0.292
• 0.380
• 0.417

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

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

George and Paul play a betting game. Each chooses an integer from 1 to 20 (inclusive) at random. If the two numbers differ by more than 3, George wins the bet. Otherwise, Paul wins the bet. Calculate the probability that Paul wins the bet.

• 0.27
• 0.32
• 0.40
• 0.48
• 0.66

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

Each week, a subcommittee of four individuals is formed from among the members of a committee comprising seven individuals. Two subcommittee members are then assigned to lead the subcommittee, one as chair and the other as secretary.

Calculate the maximum number of consecutive weeks that can elapse without having the subcommittee contain four individuals who have previously served together with the same subcommittee chair.

• 70
• 140
• 210
• 420
• 840

Bowl I contains eight red balls and six blue balls. Bowl II is empty. Four balls are selected at random, without replacement, and transferred from bowl I to bowl II. One ball is then selected at random from bowl II.

Calculate the conditional probability that two red balls and two blue balls were transferred from bowl I to bowl II, given that the ball selected from bowl II is blue.

• 0.21
• 0.24
• 0.43
• 0.49
• 0.57