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February 16th, 2017, 08:30 PM   #1
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Problem

A person goes every morning at the same time at a intersection where there's a traffic light which is in green 20% of the time. Suppose each morning represents an independent essay and with constant probability every day of the week.
What is the probability that the light of the traffic light is not green for 10 consecutive mornings? Solve this question in two ways, (i) using the binomial distribution and (ii) using the geometric distribution.
Make sure they lead to the same result.

Binomial
X is Binomial with n=10 and p=0.2
P(X=0) = (10 0) * (0.2)^0 * ( 0.8 ) ^10 = 0.1074
I don't know how to solve this question using the geometric distribution

Thank you!
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February 17th, 2017, 02:50 PM   #2
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Quote:
Originally Posted by lauchagonzalez View Post
A person goes every morning at the same time at a intersection where there's a traffic light which is in green 20% of the time. Suppose each morning represents an independent essay and with constant probability every day of the week.
What is the probability that the light of the traffic light is not green for 10 consecutive mornings? Solve this question in two ways, (i) using the binomial distribution and (ii) using the geometric distribution.
Make sure they lead to the same result.

Binomial
X is Binomial with n=10 and p=0.2
P(X=0) = (10 0) * (0.2)^0 * ( 0.8 ) ^10 = 0.1074
I don't know how to solve this question using the geometric distribution

Thank you!
Why multiply by 10? Answer is correct without it.
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February 17th, 2017, 06:23 PM   #3
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Originally Posted by mathman View Post
Why multiply by 10? Answer is correct without it.
Yes, my mistake. But the final result was ok.
How can I solve this problem using geometrical distrbution?
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February 18th, 2017, 02:54 PM   #4
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Originally Posted by lauchagonzalez View Post
Yes, my mistake. But the final result was ok.
How can I solve this problem using geometrical distrbution?
Maybe: It looks messy, but it should reduce to the binomial.
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