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# Binomial expansion watch

1. Question is:

P(no fault) = (1-p)^n, p < 0.001
Where p is the probability of a single chip being fault, and n being the total number of chips produced.

b) Given that n = 200, find an approximate expression for P(not fault)
--> 1 - 200p + 19900p^2

I was able to do this. Next question is a bit confusing due to the language.

c) Company wants to achieve 92% likelihood of having no fault chips on a production run of 200 chips. Use your answer to part b to suggest a maximum value of p for this to be the case.

Tried (1 - p) = 0.92 and substituted p = 0.08. -> wrong answer.
2. (Original post by FuryBall)
Question is:

P(no fault) = (1-p)^n, p < 0.001
Where p is the probability of a single chip being fault, and n being the total number of chips produced.

b) Given that n = 200, find an approximate expression for P(not fault)
--> 1 - 200p + 19900p^2

I was able to do this. Next question is a bit confusing due to the language.

c) Company wants to achieve 92% likelihood of having no fault chips on a production run of 200 chips. Use your answer to part b to suggest a maximum value of p for this to be the case.

Tried (1 - p) = 0.92 and substituted p = 0.08. -> wrong answer.
What you tried works for a single chip. You've got 200 chips. Try solving the top equation with n = 200
3. (Original post by an_atheist)
What you tried works for a single chip. You've got 200 chips. Try solving the top equation with n = 200
I thought the point of substituting 0.08 into 1 -200p + 19900p^2 was so that it would give me the value for 200 chips. A little confused.
4. (Original post by FuryBall)
I thought the point of substituting 0.08 into 1 -200p + 19900p^2 was so that it would give me the value for 200 chips. A little confused.
IT turns out I misunderstood the question. Maybe solve the equation equal to 0.92?

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