Assume that the box contains 4 defective widgets and 13 acceptable widgets. There are 4 inspectors, each of whom selects a widget from the box at random, inspects it, and then replaces it in the box. Each inspector makes his or her inspection at a different time.
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2 hours ago
What is the probability that at least one inspector will find a defective widget?
2006-10-09 15:56:09 · 3 answers · asked by Diggler AKA The Cab Driver 1 in Science & Mathematics ➔ Mathematics
The probability that an inspector does NOT find a defective one is 13/17. So, the probability that none of the four finds a defective one is (13/17)^4.
The probability that at least one of them will find it is
1 - (13/17)^4 ~ 0.658
2006-10-09 16:14:52 · answer #1 · answered by Seshagiri 3 · 0⤊ 0⤋
prob inspec doesnt find defective widget = 13/17
Prob that no inspector finds a defective widget = (13/17)^4
Probablity at least one inspector finds a defective widget = 1-(13/17)^4
2006-10-09 16:01:02 · answer #2 · answered by vnav_in 2 · 0⤊ 0⤋
It's tricky to calculate from the angle of "at least one".
I think it's easier to try "none of the inspectors found one."
Odds of 1 inspector not picking up defect: 13/17.
Odds of 2 inspectors not picking up defect = (13/17) ^ 2
Odds of 3 inspectors not picking up defect = (13/17) ^ 3
Odds of 4 inspectors not picking up defect = (13/17) ^ 4
= 28561 / 83521 = 0.342 = 34.2%.
The odds of at least 1 inspector NOT finding one is 100% minus 34.2% = 65.8%.
2006-10-09 16:00:09 · answer #3 · answered by PJ 3 · 1⤊ 0⤋