Featured Deals:
Function Power Tool
probability question?
When a large number of mass-produced electric light switches are examined by a quality inspector 3% are defective. Find the probability that a random sample of 10 will contain
(i) exactly 5 defective switches;
(ii) at least 2 defective switches.
also
5 power tools on a store shelf containing 12 power tools do not function properly. if 2 are selected at random from the shelf was is the probability that the first is defective and the second is not
This is an example of a binomial distribution, p = 0.03, q = 0.97, number of trials = 10.
The probability of the number of good switches in the sample being 10, 9, 8,.... and so on is given by the successive terms of the expansion of the expression :
(0.97 + 0.03)^10
so the probability of 5 good / 5 defective switches in the sample is the term
10C5 (0.97)^5 (0.03)^5
The probability that at least two switches are defective is best considered from the other direction: what is the probability that there is no more than one defective switch in the sample?
The probability of no defectives in the sample is (0.97)^10.
The probability of just one defective in the sample is 10(0.97)^9 (0.03)
So the probability of 0 or 1 defective is the sum of these probabilities, or
0.73742 + 0.22807 = 0.9655
Hence, the probability that 2 or more are defective is (1 - 0.9655) = 0.0345
---------------------------------------------------------------
Probability that the first tool selected is faulty = 5 / 12
If the first one is defective, then there are 4 faulty ones in the remaining 11 tools. The probability that the next tool selected is not faulty is 7 /11.
The probability that the first one is faulty and the second one is not, therefore is (5 / 12) x (7 / 11) = 35 / 132 = 0.2652
-----------------------------------------------------------
Current EBay auctions for Function Power Tool
