A coffee and donut shop company holds a contest in which a prize may be revealed

Question

A coffee and donut shop company holds a contest in which a prize may be revealed on the inside of the rim of a paper coffee cup. The probability that each cup reveals a prize is 0.1 and winning is independent from one cup to the next. What is the probability that a customer must roll up three or more rims before winning a prize? (show your work) A medical treatment has a success rate of .8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that neither one of them will be successfully cured? (show your work) P-values are almost universally used in scientific research to evaluate evidence against null hypotheses. Criminal courts that assess evidence under the assumption that the accused is innocence follow a procedure that appears formally very similar to testing a null hypothesis. Explain how the use of p-values in court testimony lead to unfair convictions.

Explanation / Answer

13. P(winning a prize in 1 attempt) = 0.1

P(rolling thre or more rims) = P(not winning in first 3 attempts) = (1-0.1)3 = 0.729

14. P(success) = 0.8

P(not getting cured successfully) = 1-0.8 = 0.2

P(2 people not getting cured) = 0.2x0.2 = 0.04

[please post different questions separately]

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