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Chapter 5: Q T5.13. (page 337)

Researchers are interested in the relationship between cigarette smoking and lung cancer. Suppose an adult male is randomly selected from a particular population. The following table shows the probabilities of some events related to this chance process:

(a) Find the probability that the individual gets cancer given that he is a smoker. Show your work.

(b) Find the probability that the individual smokes or gets cancer. Show your work.

(c) Two adult males are selected at random. Find the probability that at least one of the two gets cancer. Show your work.

Short Answer

Expert verified

Part (a) The probability is 0.32

Part (b) The probability is 0.29

Part (c) The probability is0.2256

Step by step solution

01

Part (a) Step 1. Given

The table is:

02

Part (a) Step 2. Concept used

Probability=FavourableoutcomesTotaloutcomes

03

Part (a) Step 3. Calculation

If a person smokes, the probability of acquiring cancer is computed as follows:

P(Cancer|Smoker)=P(CancerandSmoker)/P(Smoker)=0.08/0.25=0.32

As a result, the probability is 0.32

04

Part (b) Step 1. Calculation

The likelihood that an individual will develop cancer or become a smoker is determined as follows:

P(SmokerorCancer)=1鈭�P(Notcancernorsmoker)=1鈭�0.71=0.29

As a result, the probability is 0.29

05

Part (c) Step 1. Calculation

The likelihood that at least one of the males will develop cancer is computed as follows:

P(Cancer)=P(SmokerorCancer)+P(SmokerorCancer)鈭�P(Smoker)=0.29+0.08鈭�0.14=0.12

Now,

P(Atleastoncegetscancer)=1鈭�P(2notcancer)=1鈭�(0.88)(0.88)=1鈭�0.7744=0.2256

As a result, the probability is 0.2256

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Most popular questions from this chapter

Mac or PC? A recent census at a major university revealed that40% of its students primarily used Macintosh computers (Macs). The rest mainly used

PCs. At the time of the census, 67% of the school鈥檚 students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students who said that they used PCs as their

main computers. Suppose we select a student at random from among those who were part of the census.

(a) Assuming that there were 10,000 students in the census, make a two-way table for this chance process.

(b) Construct a Venn diagram to represent this setting.

(c) Consider the event that the randomly selected student is a graduate student who uses a Mac. Write this event in symbolic form using the two events of interest that you chose in (b).

(d) Find the probability of the event described in (c). Explain your method.

Make a two-way table that displays the sample space.

Tossing coins Imagine tossing a fair coin 3 times. (a) What is the sample space for this chance

process? (b) What is the assignment of probabilities to outcomes in this sample space?

An unenlightened gambler

(a) A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes five consecutive reds occur and bets

heavily on black at the next spin. Asked why he explains that black is 鈥渄ue by the law of averages.鈥� Explain to the gambler what is wrong with this reasoning.

(b) After hearing you explain why red and black are still equally likely after five reds on the roulette wheel, the gambler moves to a poker game. He is dealt five straight red cards. He remembers what you said and assumes that the next card dealt in the same hand is equally likely to be red or black. Is the gambler right or wrong, and why?

Find P(L). Interpret this probability in context.
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