Stats HW4: Probability Thoery

The following table shows the survival experience of 1,000 males who retire at age 65: Age: # Males Surviving 65 1000 70 907 75 775 80 596 85 383 Based on these data, the probability that a 75-year-old male will survive to age 80 is:

0.769 (Given that 775 have survived to 75, the probability is 596 divided by 775)

If two events are collectively exhaustive, what is the probability that one or the other will occur?

1.00 (Definition of probabilities)

Which statement is false?

If A and B are mutually exclusive events, then P(A or B)=0 True: If P(A) = .05, then the odds against event A's occurrence are 19 to 1. The number of permutations of five things taken two at a time is 20

If P(A∩B) = 0.50, can P(A) = 0.20?

If P(A) = 0.20, then P(A∩B) cannot equal 0.50. (The given information contains a contradiction, because P(A∩B) cannot exceed P(A))

The number of unique orders in which five items (A,B,C,D,E) can be arranged is:

120 (Apply rules of counting: 5x4x3x2x1=120)

The value of 6C2 is:

15 (Formula for combinations)

Oxnard Casualty wants to ensure that their email server has 99.98 percent reliability. They will use several independent servers in parallel, each of which is 95 percent reliable. What is the smallest number of independent file servers that will accomplish the goal?

3 (1 - P(F1∩F2∩F3) = 1 - (.05) (.05) (.05) = 1 - .000125 = .999875, so 3 servers will do)

Regarding the rules of probability, which of the following statements is correct?

The probability of A and its compliment will sum to one (Rules of probability)

Regarding the probability, which of the following is correct?

When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events (Rules of Probability)

If P(A | B) = 0.40 and P(B) = 0.30, find P(A∩B).

.120 Conditional Probability: P(A | B)= (P(A∩B))/P(B) .4/.3=.120

At Dolon General Hospital, 30 percent of the patients have Medicare insurance (M) while 70 percent do not have Medicare insurance (M´). Twenty percent of the Medicare patients arrive by ambulance, compared with 10 percent of the non-Medicare patients. If a patient arrives by ambulance, what is the probability that the patient has Medicare insurance?

.4615 (Bayes Theorem) IDK how to do this

in a certain city, 5 percent of all drivers have expired licenses, 10 percent have unpaid parking tickets, and 1 percent have both. Are these events independent?

No (For independence we would require P(A)P(B) = P(A∩B))

The probabbility that event A occurs, given that event B has occured, is an example of:

conditional probability

Events A and B are mutually exclusive when:

their joint probability is zero (mutually exclusive definition)

Two events are complementary if:

they are disjoint and their probabilities sum to one (rules of probability)