In a fierce battle, not less than 70 percent of the soldiers lost one eye and not less than 75 percent lost one ear. What is the minimal possible percentage of those who simultaneously lost one ear and one eye?

• 0.4
• 0.45
• 0.55
• 0.6
• 0.65

References

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

John and Mary are taking a mathematics course. The course has only three grades: A, B, and C. The probability that John gets a B is .3. The probability that Mary gets a B is .4. The probability that neither gets an A but at least one gets a B is .1. What is the probability that at least one gets a B but neither gets a C?

• 0.3
• 0.4
• 0.5
• 0.6
• 0.7

References

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

For a bill to come before the president of the United States, it must be passed by both the House of Representatives and the Senate. Assume that, of the bills presented to these two bodies, 60 percent pass the House, 80 percent pass the Senate, and 90 percent pass at least one of the two. Calculate the probability that the next bill presented to the two groups will come before the president.

• 0.25
• 0.35
• 0.4
• 0.5
• 0.6

References

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

A student must choose exactly two out of three electives: art, French, and mathematics. He chooses art with probability 5/8, French with probability 5/8, and art and French together with probability 1/4. What is the probability that he chooses French and mathematics?

• 1/8
• 1/4
• 3/8
• 1/2
• 5/8

References

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

A student must choose one of the subjects, art, geology, or psychology, as an elective. She is equally likely to choose art or psychology and twice as likely to choose geology. What is the probability that the student chooses art or geology?

• 1/2
• 2/3
• 3/4
• 4/5
• 1

References

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

Let [math]A[/math] and [math]B[/math] be events such that [math]P(A \cap B) = 1/4[/math], [math]P(A^c) = 1/3[/math], and [math]P(B^c) = 1/2[/math]. What is [math]P(A \cup B)[/math]?

• 1/2
• 7/12
• 2/3
• 11/12
• 1

References

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

A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face. (For example, a six is three times as probable as a two.) What is the probability of getting an odd number in one throw that is not equal to 1?

• 1/6
• 1/3
• 8/21
• 9/21
• 1/2

References

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

This year, a medical insurance policyholder has probability 0.70 of having no emergency room visits, 0.85 of having no hospital stays, and 0.61 of having neither emergency room visits nor hospital stays

Calculate the probability that the policyholder has at least one emergency room visit and at least one hospital stay this year.

• 0.045
• 0.060
• 0.390
• 0.667
• 0.840

The probability that a member of a certain class of homeowners with liability and property coverage will file a liability claim is 0.04, and the probability that a member of this class will file a property claim is 0.10. The probability that a member of this class will file a liability claim but not a property claim is 0.01.

Calculate the probability that a randomly selected member of this class of homeowners will not file a claim of either type.

• 0.850
• 0.860
• 0.864
• 0.870
• 0.890

An actuary compiles the following information from a portfolio of 1000 homeowners insurance policies:

1. 130 policies insure three-bedroom homes.
2. 280 policies insure one-story homes.
3. 150 policies insure two-bath homes.
4. 30 policies insure three-bedroom, two-bath homes.
5. 50 policies insure one-story, two-bath homes.
6. 40 policies insure three-bedroom, one-story homes.
7. 10 policies insure three-bedroom, one-story, two-bath homes.

Calculate the number of homeowners policies in the portfolio that insure neither one-story nor two-bath nor three-bedroom homes.

• 310
• 450
• 530
• 550
• 570