An actuary studying the insurance preferences of automobile owners makes the following conclusions:

1. An automobile owner is twice as likely to purchase collision coverage as disability coverage.
2. The event that an automobile owner purchases collision coverage is independent of the event that he or she purchases disability coverage.
3. The probability that an automobile owner purchases both collision and disability coverages is 0.15.

Calculate the probability that an automobile owner purchases neither collision nor disability coverage.

• 0.18
• 0.33
• 0.48
• 0.67
• 0.82

Each row in the table below gives the probability that a claim frequency will equal 0, 1, 2 or 3 for a specific policy:

The probability that the sum of the claim frequencies is less than or equal to 3 is 0.95. If the claim frequency events of distinct policies are independent, determine p.

1. 0.045
2. 0.11
3. 0.45
4. 0.55
5. 1

A company sells two types of life insurance policies (P and Q) and one type of health insurance policy. A survey of potential customers revealed the following:

1. No survey participant wanted to purchase both life policies.
2. Twice as many survey participants wanted to purchase life policy P as life policy Q.
3. 45% of survey participants wanted to purchase the health policy.
4. 18% of survey participants wanted to purchase only the health policy.
5. The event that a survey participant wanted to purchase the health policy was independent of the event that a survey participant wanted to purchase a life policy.

Calculate the probability that a randomly selected survey participant wanted to purchase exactly one policy.

• 0.51
• 0.60
• 0.69
• 0.73
• 0.78

Suppose you are given the following:

1. [math]A_1, A_2, \ldots,A_n[/math] are independent events defined on a sample space [math]\Omega[/math]
2. [math]0 \lt P(A_j) \lt 1[/math] for all [math]j[/math]

Which of the following statements is always true?

• [math]\sum_{i=1}^n P(A_i) = P(A_1 \cup \cdots \cup A_n)[/math]
• [math]\sum_{i=1}^n P(A_i) \lt 1[/math]
• [math]\Omega[/math] must have at least [math]2^n[/math] points.
• [math]\Omega[/math] must have at least [math]2n[/math] points.
• [math]\sum_{i=1}^j P(A_1 \cup \ldots \cup A_j) = P(A_1 \cup \ldots \cup A_n)[/math] for [math]j \lt n [/math]

References

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