(f) A scholarship award is to be given to 2 seniors. If students are selected ra

Question

(f) A scholarship award is to be given to 2 seniors. If students are selected randomly from the entire group, what is the probability that the second senior will be the fifth selection? II. A component in a complex system has a failure rate of 22%, i.e. the probability that any one of these components will fail is 22. How many of these components must be installed so that the probability that at least one of them works (i.e. does not fail) is greater than. 999? Assume the components function independently of each other. Show all your work.

Explanation / Answer

P(fail) = 0.22

P(work) = 1 - 0.22 = 0.78

Let the total components be n

P(at least one of them works) = 1 - P(none of them works)

                                                = 1 - nC0 * 0.780 * 0.22n

                                                = 1 - 0.22n

1 - 0.22n > 0.999

or, 0.22n < 0.001

or, n > ln(0.001) / ln(0.22)

or, n > 4.56

So, the number of these components must be installed are 5

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