#### claudiocamera

##### Full Member level 4

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**repeated trial**

A box contains 1000 bulbs of which 100 is defective, two bulbs are picked at random, find the probability that both are defective.

If we perform :

The probability that the first is defective is P(1D) = 100/1000 = 0.1

The probability that the second is defective is P(2D) = 99/999 = 0.099099...

thus the probability that both are defective is P(1D)*P(2D) = (100/1000)*(99/999). I think this is the correct result.

Now if we perform by bernoulli equations:

We have n = numbers of bulbs = 1000

We have m = number of bulbs taken = 2

We have p = Probability that the bulbs are defective equals = 100/1000=0.1

Applying Bernoulli:

P(2D) = [C(n,m)]*[p^m]*[(1-p)^(n-m)] = (1000*999/2)*[(0.1)^2]*[0.9^998] this result is cleary wrong. So here comes the question, why ? what is wrong ?