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 heinsbergrelatz March 23rd, 2019 11:55 PM

Poisson problem

So i have this Poisson question, I can do part a), b) and c) but I cant seem to do d), can anyone help me do d)?

Number of physics problems that Mike tries for any given week follows a Poisson distribution with $\mu =3.$

a) what is the probability of Mike trying exactly 2 problems in any given week?
b) If we are given that Mike tries at least 8 problems in two weeks, what is the probability that he tries more than 10 problems in these two week?

Every problem that mike tries is independent of one another, and has a constant probability of 0.2 of getting the problem correct (Mike's number of tries at the problems is independent of him answering a problem correctly)

c) Mike tries 12 problems. What is the probability that he gets at most 3 problems correct?
d) What is the probability that mike answers no questions correctly in any of the given two weeks?

I can do a),b),c), but I cant seem to do d). I would appreciate the help.

 mathman March 24th, 2019 02:08 PM

The probability of getting all incorrect if n problems are tried is $.8^n$. The probability of trying n problems in two weeks is $\frac{6^ne^{-6}}{n!}$. Therefore the probability of answering no questions correctly is $\sum_{n=0}^\infty \frac{4.8^ne^{-6}}{n!}=e^{-1.2}$.

Corrected!

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