Suppose that, starting at a certain time, batteries coming off an assembly line

Question

Suppose that, starting at a certain time, batteries coming off an assembly line are examined one by one to see whether they are defective (let D = defective and N = not defective). The chance experiment terminates as soon as two nondefective batteries have been obtained.

(a) Let A denote the event that at most three batteries must be examined to terminate the chance experiment. What outcomes are contained in A?

A = {NN} A = {NN, DNN, NDN}     A = {DD, NDD, DND} A = {NN, DNN, NDN, DDNN, DNDN, NDDN} A = {DD, NDD, DND, NDN, NNDD, NDND, DNND}

(b) Let B be the event that exactly four batteries must be examined before the chance experiment terminates. What outcomes are in B?

B = {DDNN, NDDN, DNND, DNDN, NDND, DNND, NNNN, DDDD} B = {DDNN, NDDN, DNDN}     B = {DN, ND, DD, NN} B = {DDNN, NDDN, DNND, DNDN, NDND, DNND} B = {NNDD, DNND, NDND}

(c) What can be said about the number of possible outcomes for this chance experiment?
There are ---Select---a finitean or infinite number of possible outcomes.

Explanation / Answer

a) corect option is A = A = {NN, DNN, NDN} (as experiment should end when last drawn is nondefective or N and must contain at max 3 elements)

b) this means in 3 battery only 1 N should be there so that 4th will contain nondefective and process ends)

B = {DDNN, NDDN, DNDN}

c)

There are  infinite number of possible outcomes.

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