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1) The probability of a successful optical alignment in the assembly of an optical data storage product is p = 0.6. Assume the trials are independent. Round your answers to four decimal places (e.g. 98.7654).

- What is the probability that the first successful alignment requires at least four trials?

2) In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.2.

(a) What is the probability that 4 or more people will have to be tested until 2 of them with the gene are detected? Round your answer to three decimal places (e.g. 0.987).

(b) How many people are expected to be tested until 2 of them with the gene are detected?

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Category:- Statistics and Probability
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