GATE CS 2014 Set 2 — Question 11
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Question
The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functional be denoted by . Then _____________.
Correct answer
11.85 to 11.95
Solution
Total number of computers .
Number of working computers .
Number of non-working computers .
Number of computers inspected .The system is deemed functional if at least 3 of the 4 inspected computers are working. This means either 3 are working or 4 are working.Total ways to choose 4 computers from 10:Case 1: Exactly 3 working computers are chosen.
We choose 3 from the 4 working and 1 from the 6 non-working.Case 2: Exactly 4 working computers are chosen.
We choose 4 from the 4 working and 0 from the 6 non-working.Total favorable outcomes = .Probability :We need to find :The value lies within the range 11.85 to 11.95.
Number of working computers .
Number of non-working computers .
Number of computers inspected .The system is deemed functional if at least 3 of the 4 inspected computers are working. This means either 3 are working or 4 are working.Total ways to choose 4 computers from 10:Case 1: Exactly 3 working computers are chosen.
We choose 3 from the 4 working and 1 from the 6 non-working.Case 2: Exactly 4 working computers are chosen.
We choose 4 from the 4 working and 0 from the 6 non-working.Total favorable outcomes = .Probability :We need to find :The value lies within the range 11.85 to 11.95.
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