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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鈥檛 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脳0.010.99脳0.01+0.02脳0.99=0.010.01+0.02=13

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Most popular questions from this chapter

Question: Use both the sample space (2.4) and the sample space (2.5) to answer the following questions about a toss of two dice.

(a) What is the probability that the sum is 鈮� 4?

(b) What is the probability that the sum is even?

(c) What is the probability that the sum is divisible by 3?

(d) If the sum is odd, what is the probability that it is equal to 7?

(e) What is the probability that the product of the numbers on the two dice is 12?

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 鈥檚 and show that you then have an identity.

Find the number of ways of putting2particles in4boxes according to the three kinds of statistics.

A bit (meaning binary digit) is 0 or 1. An ordered array of eight bits (such as01101001) is a byte. How many different bytes are there? If you select a byte at random, what is the probability that you select 11000010? What is the probability thatyou select a byte containing three 1鈥檚 and five 0鈥檚?

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