Letters problem

[trackgirl000]

HELP!
Suppose that a letter sent from City A has a probabilty 0.8 of reaching City B in three days.
a. Three letters are sent from City A to City B on three different occations. What is the probability that exactly two letters reach City B in three days?
b. If the three letters are mailed together at the same time and location, how does the conclusion in part (a) change? explain.

thank you!

 

[mark07]

If you assume that each letter sent is handled independently from others, it's a binomial distribution problem.

Suppose n letters are sent. Let X denote the number of letters sent from A that reach to B within 3 days. Then

\(\displaystyle \L P(X=k) = \left( \begin{matrix} n \\ k \end{matrix} \right) 0.8^k 0.2^{n-k}\)

Part (a) seems to suggest that you can use this, since independence is given by saying "different occasions".

Part (b) does not have independence since they are handled at the same time. What I would assume is that either all letters reach to B within 3 days or none of them reach on time. So my answer to (b) is 0.