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# Probability, Combinations and Permutations

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Find the indicated probability
1) The table below describes the smoking habits of a group of asthma sufferers.
Nonsmoker, Occasional smoker, Regular smoker, Heavy smoker, Total
Men, 431, 50, 71, 49, 601
Women, 382, 48, 86, 39, 555
Total, 813, 98, 157, 88, 1156

If one of the 1156 people is randomly selected. find the probability that the person is a man or a havey smoker.

2) In one town, 66% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? round to the nearest thousandth if necessary.

Binomial Probability: Find the indicated probability
3) The brand name of a certain chain of coffee shops has a 46% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 8 Coffleton residents. Find the probability that exactly 4 of the 8 Coffleton residents recognize the brand name.

Find the indicated probability
4) A IRS auditor randomly selects 3 tax returns from 49 returns of which 7 contain errors. What is the probability that she selects none of those containing errors? Round to four decimal places.

5) Of the 64 people who answered "yes" to a question, 6 were male. Of the 70 people that answered "no" to the question, 8 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male?

Provide an appropriate response
6) In a game, you have a 1/36 probability of winning \$85 (this is your profit, after you already paid in) and a 35/36 probability of losing \$4. What is your expected value?

Find the indicated probability. Round to the nearest thousandth.
7) In a batch of 8,000 clock radios 2% are defective. A sample of 11 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected?

8) In a certain lottery, five different numbers between 1 and 20 inclusive are drawn. These are the winning numbers. To win the lottery, a person must select the correct five numbers in the same order in which they were drawn. What is the probability of winning?

9) A tourist in France wants to visit six different cities. How many routes are possible?

10) 12 wrestlers compete in a competition. if each wrestler wrestles one match with each other wrestler what are the total numbers of matches?

https://brainmass.com/statistics/probability-theory/probability-combinations-permutations-620023

#### Solution Preview

1)
Add the numbers in the Men row and Heavy smoker column.
431 + 50 + 71 + 49 + 39 = 640
divide by the total number of people surveyed (1156).

640 / 1156 = 0.554