The security system at an IT office is composed of 10 computers of which…
2014
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 \(p\). Then 100\(p\)_____________ = .
Attempted by 41 students.
Show answer & explanation
Correct answer: 11.85 to 11.95
Key idea: count the favorable selections and divide by the total selections.
Total ways to choose 4 computers from 10: C(10,4) = 210
Ways to get exactly 3 working among the 4 inspected: choose 3 of the 4 working and 1 of the 6 non-working: C(4,3)·C(6,1) = 4·6 = 24
Ways to get all 4 working: choose all 4 working: C(4,4) = 1
Total favorable selections = 24 + 1 = 25.
Probability that the system is deemed functional: p = 25/210 = 5/42 ≈ 0.1190476
Therefore, 100p = 250/21 ≈ 11.9047619.
Final value (exact): 100p = 250/21. Final value (rounded to two decimal places): 11.90.