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The probability that a male develops some form of cancer in his lifetime is 0.4567. The probability that a male has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51. Some of the following questions do not have enough information for you to answer them. Write 鈥渘ot enough information鈥� for those

answers. Let C = a man develops cancer in his lifetime and P = man has at least one false positive.

a. P(C) = ______

b. P(P|C) = ______

c. P(P|C') = ______

d. If a test comes up positive, based upon numerical values, can you assume that man has cancer? Justify numerically and explain why or why not.

In a recent issue of the IEEE Spectrum, $84$engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let X = the length (in days) of an engineering conference.

a. Organize the data in a chart.

b. Find the median, the first quartile, and the third quartile.

c. Find the $65th$percentile.

d. Find the $10th$percentile.

e. Construct a box plot of the data.

f. The middle $50\%$of the conferences last from _______ days to _______ days.

g. Calculate the sample mean of days of engineering conferences.

h. Calculate the sample standard deviation of days of engineering conferences.

i. Find the mode.

j. If you were planning an engineering conference, which would you choose as the length of the conference: mean; median; or mode? Explain why you made that choice.

k. Give two reasons why you think that three to five days seem to be popular lengths of engineering conferences.

Given events G and H: P(G) = 0.43; P(H) = 0.26; P(H AND G) = 0.14

a. Find P(H OR G).

b. Find the probability of the complement of event (H AND G).

c. Find the probability of the complement of event (H OR G).

Given events J and K: P(J) = 0.18; P(K) = 0.37; P(J OR K) = 0.45

a. Find P(J AND K).

b. Find the probability of the complement of event (J AND K).

c. Find the probability of the complement of event (J OR K).

Use the following information to answer the next two exercises. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled.

Suppose that you randomly draw two cards, one at a time, with replacement.

Let G1 = first card is green

Let G2 = second card is green

a. Draw a tree diagram of the situation.

b. Find P(G1 AND G2).

c. Find P(at least one green).

d. Find P(G2|G1).

e. Are G2 and G1 independent events? Explain why or why not.

Suppose that you randomly draw two cards, one at a time, without replacement.

G1 = first card is green

G2 = second card is green

a. Draw a tree diagram of the situation.

b. Find P(G1 AND G2).

c. Find P(at least one green).

d. Find P(G2|G1).

e. Are G2 and G1 independent events? Explain why or why not.

Suppose that you randomly draw two cards, one at a time, without replacement.

$G1$= first card is green

$G2$= second card is green

a. Draw a tree diagram of the situation.

b. Find $P(G1ANDG2)$.

c. Find $P$(at least one green).

d. Find $P\left(G2\right|G1)$.

e. Are $G2$ and $G1$ independent events? Explain why or why not

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are female is \(48.60\). Of the females, \(5.03%\) are age \(19\) and under; \(81.36%\) are age \(20鈥�64; 13.61%\) are age \(65\) or over. Of the licensed U.S. male drivers, \(5.04%\) are age \(19\) and under; \(81.43%\) are age \(20鈥�64; 13.53%\) are age \(65\) or over.

Compute the following:

a. Construct a table or a tree diagram of the situations.

b. Find \(P\)(driver is female)

c. Find \(P\)(driver is age \(65\) or over|driver is female).

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are female is 48.60. Of the females, 5.03% are age 19 and under; 81.36% are age 20鈥�64; 13.61% are age 65 or over. Of

the licensed U.S. male drivers, 5.04% are age 19 and under; 81.43% are age 20鈥�64; 13.53% are age 65 or over.

Suppose that 10,000 U.S. licensed drivers are randomly selected.

a. How many would you expect to be male?

b. Using the table or tree diagram, construct a contingency table of gender versus age group.

c. Using the contingency table, find the probability that out of the age 20鈥�64 group, a randomly selected driver is female.

Suppose that $10,000U.S.$licensed drivers are randomly selected.

a. How many would you expect to be male?

b. Using the table or tree diagram, construct a contingency table of gender versus age group.

c. Using the contingency table, find the probability that out of the age $20-64$group, a randomly selected driver is female.