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Chapter 15: Q19P (page 736)

Suppose it is known that 1% of the population have a certain kind of cancer. It is also known that a test for this kind of cancer is positive in 99% of the people who have it but is also positive in 2% of the people who do not have it. What is the probability that a person who tests positive has cancer of this type?

Short Answer

Expert verified

Answer

The probability that a person who tests positive has cancer is 13.

Step by step solution

01

Given Information

Probability of having cancer is 0.01, the probability of positive test result is and false positive is 0.02

02

Definition of Independent Event

The events are said to be independent when the occurrence or non-occurrence of any event does not have any effect on the occurrence or non-occurrence of the other event.

03

Drawing the tree diagram for the situation

Draw the tree diagram depicting the person have cancer and don’t have cancer and it tested positive or negative and show respective probability.

04

Finding the probability that a person who tests positive has cancer

Find the probability that that a person who tests positive has cancer using the Bayes Theorem.

PTestPositiveHasCancer=PHascancerandtestpositivePTestPositive=0.99×0.010.99×0.01+0.02×0.99=0.010.01+0.02=13

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Most popular questions from this chapter

Use Bayes’ formula (3.8) to repeat these simple problems previously done by usinga reduced sample space.

(a) In a family of two children, what is the probability that both are girls if at

least one is a girl?

(b) What is the probability of all heads in three tosses of a coin if you know that

at least one is a head?

Prove (3.1) for a nonuniform sample space. Hints: Remember that the probability of an event is the sum of the probabilities of the sample points favorable to it. Using Figure 3.1, let the points in A but not in AB have probabilities p1, p2, ... pn, the points in have probabilities pn+1, pn+2, .... + pn+k, and the points in B but not in AB have probabilities pn+k+1, pn+k+2, ....pn+k+l. Find each of the probabilities in (3.1) in terms of the ’s and show that you then have an identity.

A so-called 7-way lamp has three 60-watt bulbs which may be turned on one or two or all three at a time, and a large bulb which may be turned to 100 watts, 200 watts or300 watts. How many different light intensities can the lamp be set to give if the completely off position is not included? (The answer is not 7.)

The following measurements ofx and yhave been made.

x:5.1,4.9,5.0,5.2,4.9,5.0,4.8,5.1y:1.03,1.05,0.96,1.00,1.02,0.95,0.99,1.01,1.00,0.99

Find the mean value and the probable error ofx,  y,  x+y,  xy,  x3sinyand.ln(x)

A trick deck of cards is printed with the hearts and diamonds black, and the spades and clubs red. A card is chosen at random from this deck (after it is shuffled). Find the probability that it is either a red card or the queen of hearts. That it is either a red face card or a club. That it is either a red ace or a diamond.
See all solutions

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