Suppose that starting at a certain time batteries coming off

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 a nondefective bettery is obtained.

a. Give five possible outcomes for this chance experiment.

b. What can be said about the number of outcomes in the sample space?

c. What outcomes are in the event E, that the number of battery examined is an number?

Solution

a)

The possible outcome may be that the nondefective battery is obtained in 1st attempt, then the process will terminate at the first step only. If the nondefective battery is obtained in second step, the process will terminate there and so on.

So, the possible outcomes can be written as - (N, DN, DDN, DDDN, DDDDN,...............).

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b)

The sample space size can not be determined as it may be infinite. The process won\'t stop till we get a nondefective battery. So, there is possibility that there is no nondefective battery. So, the sample space conatins the infinite elements as shown below -

S = {N, DN, DDN, DDDN, DDDDN, DDDDDN, DDDDDDN,...........................DDDDDDDDDDDDDDD......}

So, it has infinte sample size.

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c)

For the number of batteries examined to be even, there must be 2 or 4 or 6 and so on. And also each experiment terminates with an N. So the possible outcomes are DN, DDDN, DDDDDN.... and so on.