Suppose the following holds:
- [math]A [/math] is independent of both [math]B [/math] and [math]C[/math]
- [math]\operatorname{P}(B \cup C ) = 0.7 [/math]
- [math]\operatorname{P}(A) = 0.5 [/math], [math]\operatorname{P}(B) = 0.5 [/math] and [math]\operatorname{P}(C) = 0.3 [/math]
- [math]\operatorname{P}(A \cup B \cup C) = 1[/math]
Determine [math]\operatorname{P}(A \cap B \cap C) [/math].
- 0
- 0.1
- 0.15
- 0.2
- 0.3
- Created by Admin, May 31'22
Each row in the table below gives the probability that a claim frequency will equal 0, 1, 2 or 3 for a specific policy:
0 | 1 | 2 | 3 |
---|---|---|---|
0.55 | 0.45 | 0 | 0 |
p | 1-p | 0 | 0 |
0.6 | 0.3 | 0.05 | 0.05 |
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.
- 0.045
- 0.11
- 0.45
- 0.55
- 1
- Created by Admin, May 31'22
If [math]A [/math] is independent of itself, what are the possible values for [math]\operatorname{P}(A)[/math] ?
- 0 only
- 1 only
- 0 or 1 only
- 1/2 only
- Impossible to determine
- Created by Admin, May 31'22
You are given the following:
- Events [math]A[/math] and [math]B[/math] are independent
- [math]\operatorname{P}[A-B] + \operatorname{P}[B-A][/math] = 0.5
- [math]\operatorname{P}[A] [/math] = 0.65
Determine [math]\operatorname{P}[A \cap B][/math].
- 0.2275
- 0.3
- 0.325
- 1/3
- 0.5
- Created by Admin, May 31'22
An insurance company pays hospital claims. The number of claims that include emergency room or operating room charges is 85% of the total number of claims. The number of claims that do not include emergency room charges is 25% of the total number of claims. The occurrence of emergency room charges is independent of the occurrence of operating room charges on hospital claims.
Calculate the probability that a claim submitted to the insurance company includes operating room charges.
- 0.10
- 0.20
- 0.25
- 0.40
- 0.80
- Created by Admin, Apr 30'23
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:
- No survey participant wanted to purchase both life policies.
- Twice as many survey participants wanted to purchase life policy P as life policy Q.
- 45% of survey participants wanted to purchase the health policy.
- 18% of survey participants wanted to purchase only the health policy.
- 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
- Created by Admin, Apr 30'23
Let A, B, and C be events such that [math]\operatorname{P}[A] = 0.2[/math], [math]\operatorname{P}[B] = 0.1 [/math], and [math]\operatorname{P}[C] = 0.3 [/math]. The events A and B are independent, the events B and C are independent, and the events A and C are mutually exclusive.
Calculate [math]\operatorname{P}[A \cup B \cup C] . [/math]
- 0.496
- 0.540
- 0.544
- 0.550
- 0.600
- Created by Admin, Apr 30'23
Events [math]E[/math] and [math]F[/math] are independent. [math]\operatorname{P}[E] = 0.84[/math] and [math]\operatorname{P}[F] = 0.65[/math].
Calculate the probability that exactly one of the two events occurs.
- 0.056
- 0.398
- 0.546
- 0.650
- 0.944
- Created by Admin, Apr 30'23
Two fair dice, one red and one blue, are rolled.
Let A be the event that the number rolled on the red die is odd.
Let B be the event that the number rolled on the blue die is odd.
Let C be the event that the sum of the numbers rolled on the two dice is odd. Determine which of the following is true.
- A, B, and C are not mutually independent, but each pair is independent.
- A, B, and C are mutually independent.
- Exactly one pair of the three events is independent.
- Exactly two of the three pairs are independent.
- No pair of the three events is independent.
- Created by Admin, Apr 30'23
In any 12-month period, the probability that a home is damaged by fire is 20% and the probability of a theft loss at a home is 30%. The occurrences of fire damage and theft loss are independent events.
Calculate the probability that a randomly selected home will either be damaged by fire or will have a theft loss, but not both, during the next year.
- 0.30
- 0.38
- 0.44
- 0.50
- 0.56
- Created by Admin, May 09'23