Question

2. (a) A company has a security system comprising four electronic devices (A, B, C and D) which operate independently .Each device has a probability of failure of 0, 1. The four electronic devices are arranged so the whole system operates properly if at least one of A or B functions and at least one of C or D functions. What is the probability that the whole system operates properly. [2] (b) A market survey worker is required to interview a quota of two retailers each day. Unfortunately retailers are not always prepared to be interviewed, in fact there is a 0, 4 probability that a given retailer will refuse. If the worker can approach a maximum of four retailers in a day, what is the probability that (i) He will have completed his quota after visiting (a) 2 retailers [1] (b) 3 retailers [1] 

          2. (a) A company has a security system comprising four electronic devices (A, B, C and D) which operate independently .Each device has a probability of failure of 0, 1. The four electronic devices are arranged so the whole system operates properly if at least one of A or B functions and at least one of C or D functions. What is the probability that the whole system operates properly. [2]

(b) A market survey worker is required to interview a quota of two retailers each day. Unfortunately retailers are not always prepared to be interviewed, in fact there is a 0, 4 probability that a given retailer will refuse. If the worker can approach a maximum of four retailers in a day, what is the probability that

(i) He will have completed his quota after visiting
(a) 2 retailers [1]
(b) 3 retailers [1]
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2. (a) A company has a security system comprising four electronic devices (A, B, C and D) which operate independently .Each device has a probability of failure of 0, 1. The four electronic devices are arranged so the whole system operates properly if at least one of A or B functions and at least one of C or D functions. What is the probability that the whole system operates properly. [2] (b) A market survey worker is required to interview a quota of two retailers each day. Unfortunately retailers are not always prepared to be interviewed, in fact there is a 0, 4 probability that a given retailer will refuse. If the worker can approach a maximum of four retailers in a day, what is the probability that (i) He will have completed his quota after visiting (a) 2 retailers [1] (b) 3 retailers [1]

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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(a) A company has a security system comprising four electronic devices (A, B, C and D) which operate independently. Each device has a probability of failure of 0, 1. The four electronic devices are arranged so the whole system operates properly if at least one of A or B functions and at least one of C or D functions. What is the probability that the whole system operates properly? (b) A market survey worker is required to interview a quota of two retailers each day. Unfortunately retailers are not always prepared to be interviewed, in fact there is a 0, 4 probability that a given retailer will refuse. If the worker can approach a maximum of four retailers in a day, what is the probability that (i) He will have completed his quota after visiting (a) 2 retailers (b) 3 retailers
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Transcript

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00:01 For the given question, solving part a, we are having here the information about the company has security system, security system for four electronic devices which are named as a, b, c and d operated independently and here we need to find the probability that whole system operate properly.
00:30 So let's solve our question.
00:31 So first of all, the given whole system work properly if at least a or b or at least c or d works.
00:53 So here the probability will be for system work work that will be finite from probability of a union b intersection probability of c union union b.
01:18 So this will be the probability which we will have to find here.
01:21 And now since all electron devices run independently, so we will use the law of independent event, independent event law.
01:36 So by using this law, we can say probability for the first part a union of p will be equal to probability of a added by probability of b minus probability of b.
01:50 Of a into or multiplied by probability of b.
01:56 So let's put down our values here.
01:59 Values are 0 .9 for b minus 0 .99 multiplied by 0 .9 again.
02:11 So our final value will be equal to 0 .99 for probability of event a union of p.
02:20 And now let's find out our next event probability of c union of b will be equal to probability of event c plus probability of event d minus probability of event c multiplied by probability of event d.
02:39 So again we are having the same values for these event also.
02:43 So 9 .0 .9 minus 0 .9 multiplied by 0 .9 .9.
02:50 So the value will be equal to 0 .9 .9.
02:53 So now we have to put these two values in our equation.
03:02 This is d.
03:05 So as our probability for system work works will be equal to probability of event a union b, intersection of probability of event c union b.
03:26 So this will be as 9 .0 .99.
03:31 99 multiplied by 0 .99 will be equal to 0 .981...
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