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Warm-up: A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the following probabilities. 1st two are both good At least one of the first 3 works The first four you pick all work You have to pick 5 batteries in order to find one that works.

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Baye’s & At Least one

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**On January 28, 1986, Space Shuttle Challenger exploded on takeoff**

On January 28, 1986, Space Shuttle Challenger exploded on takeoff. All seven crew members were killed. Following the disaster, scientists and statisticians helped analyze what went wrong. They determined that the failure of O-ring joints in the shuttle’s booster rockets was to blame. Under the cold conditions that day, experts estimated that the probability that an individual O-ring joint would function properly was But there were six of these O-ring joints, and all six had to function properly for the shuttle to launch safely. Find the probability that the shuttle would launch safely under similar conditions.

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**What is the probability that in a family of 3 children there is at least one girl?**

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Many people who come to clinics to be tested for HIV, the virus that causes AIDS, don’t come back to learn the test results. Clinics now use “rapid HIV tests” that give a result while the client waits. In a clinic in Malawi, for example, use of rapid tests increased the percent of clients who learned their test results from 69% to 99.7%. The trade-off for fast results is that rapid tests are less accurate than slower lab tests. Applied to people who have no HIV antibodies, one rapid test has probability about of producing a false positive. What is the chance that at least one false positive will occur?

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**Two mutually exclusive events can never be independent!**

Let’s consider two mutually exclusive events. A – the person is male B- the person is pregnant Do you agree they are mutually exclusive? Independence:

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**Assumption of Independence**

If random sample of size n is taken from population of size N, theoretical probability of successive selections calculated with replacement and without replacement differ by insignificant amounts when n is small compared to N. Independence can be assumed if n is no larger than 5% of N.

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P(smoking) = .34 What’s the probability that 3 people smoke?

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**E1= new monitor works. P(E1)=0. 98 E2=mouse works. P(E2) = 0**

E1= new monitor works P(E1)=0.98 E2=mouse works P(E2) = 0.98 E3=disk drive works P(E3) = 0.94 E4= processor works P(E4) = 0.99 P(Operates correctly) = P(all work except Monitor) =

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A study found that 44% of college students engage in binge drinking, 37% drink moderately, 19% abstain entirely. Another study found that among binge drinkers 17% have been involved in an alcohol-related car accident, while among non-bingers only 9% have been involved in such accidents. Find the probability that a student who has an alcohol-related car accident is a binge drinker.

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**Dan’s Diner employs three dishwashers**

Dan’s Diner employs three dishwashers. Al washes 40% of the dishes and breaks only 1% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 1% of hers, but Chuck breaks 3% of the dishes he washes. You go to Dan’s for supper one night and hear a dish break at the sink. What’s the probability that Chuck is on the job?

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Video-sharing sites, led by YouTube, are popular destinations on the Internet. About 27% of adult Internet users are 18 to 29 years old, another 45% are 30 to 49 years old, and the remaining 28% are 50 and over. The Pew Internet and American Life Project finds that 70% of Internet users aged 18 to 29 have visited a video-sharing site, along with 51% of those aged 30 to 49 and 26% of those 50 or older. What is the probability that an adult internet users visits video-sharing sites? What is proportion of adult Internet users who visit video-sharing sites are aged 18 to 29?

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**Box 1 has 2 red balls and 3 green. Box 2 has 4 red and 1 green**

Box 1 has 2 red balls and 3 green. Box 2 has 4 red and 1 green. One ball is randomly selected fromn Box 1 and put in box 2. What’s the probability of a ball drawn from box 2 is green?

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**Suppose that a new Internet company Mumble**

Suppose that a new Internet company Mumble .com requires all employees to take a drug test. Mumble.com can afford only the inexpensive drug test – the one with a 5% false-positive rate and a 10% false-negative. Suppose that 10% of those who work for Mumble.com are using the drugs for which Mumble is checking. Probability that the employee both uses drugs and tests positive. What is the probability that the employee does not use drugs but tests positive anyway? What is the probability that the employee tests positive? If we know that a randomly chosen employee has tested positive, what is the probability that he or she uses drugs?

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Homework

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