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January 29th, 2019, 05:42 PM   #1
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probability question

A postal employee has 2 letters to deliver to 2 different homes, but randomly delivers the letters on a block with three houses. What is the probability that:

(a) Exactly one of the letters will be delivered properly?

(b) Both letters will be delivered properly?

(c) None of the letters will be delivered properly?

(d) At least one of the letters will be delivered properly?

Thank you!
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January 29th, 2019, 06:05 PM   #2
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The number of letters properly delivered, $n$, is a binomially distributed random variable.

$P[\text{a single letter is properly delivered}] = \dfrac 1 3$

Thus the parameters of the distribution are $n=2,~p=\dfrac 1 3$

$P[k] = \dbinom{2}{k}\left(\dfrac 1 3\right)^k \left(1 - \dfrac 1 3\right)^{2-k}$

a) P[1]

b) P[2]

c) P[0]

d) 1 - P[0]

you can do the plug and chug
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