Exam 5: Probability

If event A occurs, then its complement (A´) will also occur.

Given the contingency table shown here, find P(A or M). Cell Phone Service Provider County Sprint (S) AT\&T (A) Verizon (I) Row Total Macomb(M) 17 25 8 50 Oakland(O) 19 38 13 70 Wayne(W) 24 37 19 80 ColTotal 60 100 40 200

Given the contingency table shown here, find the joint probability that a call sampled at random out of this population is local and 2-5 minutes long. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Call Length (minutes) }$ Type of Phone Call 0-1 2-5 6+ Total Local 150 250 100 500 Long Distance 170 120 10 Total 320 370 110 300

Given the contingency table shown here, find P(B | A). $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Age }$ Absences Under 25(A) 25 or More Row Total Under 2 days (B) 50 40 90 2 or more days 30 80 110 Column Total 80 120 200

Given the contingency table shown here, find P(G | M). Vehicle Type Somerset (S) Oakland (O) Great Lakes (G) Row Total Car (C) 44 49 36 129 Minivan (M) 21 15 18 54 Full-Size Van (F) 2 3 3 8 SUV (I) 19 27 26 72 Truck (T) 14 6 17 37 Col Total 100 100 100 400

Given the contingency table shown here, find P(W?S). Cell Phone Service Provider County Sprint (S) AT\&T (A) Verizon (I) Row Total Macomb(M) 17 25 8 50 Oakland(O) 19 38 13 70 Wayne(W) 24 37 19 80 ColTotal 60 100 40 200

Two events are complementary (i.e., they are complements) if:

When the outcome of a random experiment is a continuous measurement, the sample space is described by a rule instead of listing the possible simple events.

Ramjac Company wants to set up k independent file servers, each capable of running the company's intranet. Each server has average "uptime" of 98 percent. What must k be to achieve 99.999 percent probability that the intranet will be "up"?

Given the contingency table shown here, find P(V). Cell Phone Service Provider County Sprint (S) AT\&T (A) Verizon (I) Row Total Macomb(M) 17 25 8 50 Oakland(O) 19 38 13 70 Wayne(W) 24 37 19 80 ColTotal 60 100 40 200

From the following tree, find the probability that a randomly chosen person will get the flu vaccine and will also get the flu.

The following table gives a classification of the 10,000 shareholders of Oxnard Xylophone Distributors, Inc. A few numbers are missing from the table. Given that a shareholder holding 500-999 shares is picked, there is a 0.625 probability that the shareholder will be a woman. Consequently, what is the number of men holding 1000 or more shares? Shareholders -499 500-999 1,000+ Total Men 3,000 4,000 Women 2,000 4,800 Joint Accounts 0 1,000 200 1,200 Total 5,000 4,000 1,000 10,000

The following table shows the survival experience of 1,000 males who retire at age 65: Age Number of Males Surviving 65 1,000 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:

In a contingency table, the probability of the union of two events is found by taking the frequency of the intersection of the two events and dividing by the total.

Given the contingency table shown here, what is the probability that a mother smoked during pregnancy if her education level was below high school? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Smoked during }$$\quad$ $\text { Didn't Smoke during }$ Mother's Education Pregnancy Pregnancy Row Total Below High School 393 640 1,033 High School 560 1,370 1,930 Some College 121 635 756 College Degree 48 550 598 Col Total 1,122 3,209 4,331

Given the contingency table shown here, if a call is sampled at random, find the marginal probability that the call is long distance. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Call Length (minutes) }$ Type of Phone Call 0-1 2-5 6+ Total Local 150 250 100 500 Long Distance 170 120 10 Total 320 370 110 300

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

Given the contingency table shown here, find P(A₁?A₂). Row Total 12 26 42 68 148 14 28 44 64 150 18 32 47 72 169 Col Total 44 86 133 204 467

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

If P(A) = .20 then the odds against event A's occurrence are 4 to 1.