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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.

Short Answer

Expert verified

a) Probability of C P(C) is 0.4567

b) P(P|C)cannot be determined

c) P(P|C')cannot be determined

d) This statement is unpredictable and unjustified.

Step by step solution

01

(a) To find Probability of P(C)

Following are the details given in the question

The probability that a male affected by cancer in his lifetime is 0.4567

The probability that a male has at least one false positive test result is 0.51

As given C implies the male develops some form of cancer in his lifetime.

Therefore, Probability of C is

P(C)=0.4567.

02

To find P(P|C)

Following are the details given in the question

The probability that a male affected by cancer in his lifetime is 0.4567

The probability that a male has at least one false positive test result is 0.51

So, here we need P(P|C). But the given information is not sufficient to solve.

Therefore, P(P|C)cannot be determined.

03

To find P(P|C')

Following are the details given in the question

The probability that a male affected by cancer in his lifetime is 0.4567

The probability that a male has at least one false positive test result is 0.51

So, here we need P(P|C'). But the given information is not sufficient to solve.

Therefore, P(P|C')cannot be determined.

04

To justify

If a test comes up positive, assume that man has cancer or not.

Following are the details given in the question

The probability that a male affected by cancer in his lifetime is 0.4567

The probability that a male has at least one false positive test result is 0.51

Hence, 0.51 man has one wrong positive test result.

We cannot assume and justify the man has cancer or not.

Therefore,

This statement is unpredictable and unjustified.

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Most popular questions from this chapter

Use the following information to answer the next 12exercises. The graph shown is based on more than 170,000interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

Find the probability that an Emotional Health Index Score is 82.7

Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data: Table 3.2.


Speeding violation in the last yearNo speeding violation in the last yearTotal
Uses cell phone while driving25280305
Does not use cell phone while driving45405450
Total70685755

The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and

685. Notice that 305 + 450 = 755 and 70 + 685 = 755.

Calculate the following probabilities using the table.

a. Find P(Driver is a cell phone user).

b. Find P(driver had no violation in the last year).

c. Find P(Driver had no violation in the last year AND was a cell phone user).

d. Find P(Driver is a cell phone user OR driver had no violation in the last year).

e. Find P(Driver is a cell phone user GIVEN driver had a violation in the last year).

f. Find P(Driver had no violation last year GIVEN driver was not a cell phone user)

Use the following information to answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three.

What does P(E|M) mean in words?

A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(B AND D) = 0.20.

a. Find P(B|D).

b. Find P(D|B).

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d. Are B and D mutually exclusive?

Use the following information to answer the next 12exercises. The graph shown is based on more than 1,70,000interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

What occupation has the highest emotional index score?

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