Question

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 “not enough information” 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

a) Probability of C P(C) is 0.4567

b) $P\left(P\right|C)$cannot be determined

c) $P\left(P\right|C\text{'})$cannot be determined

d) This statement is unpredictable and unjustified.

Step-by-step solution

(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

$P\left(C\right)=0.4567$.

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 $P\left(P\right|C)$. But the given information is not sufficient to solve.

Therefore, $P\left(P\right|C)\hspace{0.17em}$cannot be determined.

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 $P\left(P\right|C\text{'})$. But the given information is not sufficient to solve.

Therefore, $P\left(P\right|C\text{'})$cannot be determined.

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.