7. If you flip a fair (balanced) coin 6 times, how many different ways could you

Question

7. If you flip a fair (balanced) coin 6 times, how many different ways could you get three tails? (You do not need to list them.) How many different outcomes are possible in total? What is the probability that you will get exactly three tails?



8. A researcher has thirty 6-month old microarray chips. Suppose 20% of chips go bad six months. So, he suspects six of the thirty have gone bad. He selects four of them at random, and will use all four in an experiment, what is the probability that at least one of them will be defective, assuming his suspicions are true?

Explanation / Answer

7. Combination of 6 things 3 at a time 6!/3!(6-3)!= 20 2^6= 64 20 * 0.5^6= 0.3125 8. If there is a .2 chance a chip will fail, there is a 1-.2= .8 chance it won't. Probability all four won't fail is .8^4= 0.4096. So the chance at least one will fail is 1-.4096= 0.5904.

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