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January 29th, 2019, 04:42 PM  #1 
Newbie Joined: Jul 2015 From: N/A Posts: 17 Thanks: 0  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! 
January 29th, 2019, 05:05 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,408 Thanks: 1309 
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 $n=2,~p=\dfrac 1 3$ $P[k] = \dbinom{2}{k}\left(\dfrac 1 3\right)^k \left(1  \dfrac 1 3\right)^{2k}$ a) P[1] b) P[2] c) P[0] d) 1  P[0] you can do the plug and chug 

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