Question

Assume that you have an old "buggy" Pentium processor. The probability, p, of a given calculation failing is 1 in 100,000. Failed calculations are independent. Given 100,000 calculations, what is the probability that 1 calculation will have failed? Show your work.​

Answer 1

The answer is (99,999/100,000)^(99,999).

Answer 2

Answer: So the probability that exactly one calculation will fail out of 100,000 calculations is (99,999/100,000)^(99,999).

Explanation: The probability that a given calculation will fail is p = 1/100,000. Therefore, the probability that a calculation will not fail is 1-p = 1 - 1/100,000 = 99,999/100,000.

If we have 100,000 calculations, the probability that exactly one calculation will fail is given by the binomial probability formula:

P(exactly 1 success) = (100,000 choose 1) * p^1 * (1-p)^(100,000-1)

Plugging in the values, we get:

P(exactly 1 success) = (100,000 choose 1) * (1/100,000) * (99,999/100,000)^(99,999)

This simplifies to:

P(exactly 1 success) = (100,000) * (1/100,000) * (99,999/100,000)^(99,999)

Which further simplifies to:

P(exactly 1 success) = 1 * (99,999/100,000)^(99,999)

And finally:

P(exactly 1 success) = (99,999/100,000)^(99,999)

So the probability that exactly one calculation will fail out of 100,000 calculations is (99,999/100,000)^(99,999).