Help on a probability distribution question?

Question

Hey I've done all parts to this question apart from part iv. I have no clue how to do as they could use either 2 tickets or 1 ticket.

https://www.dropbox.com/s/wyevuaiomf32ikl/Screenshot%202014-03-13%2009.38.52.png

Answer 1

Divide into cases. We either have (i) $5$ orders, all singles or (ii) $4$ orders, a double and $3$ singles or (iii) $3$ orders, $2$ doubles and a single.

Calculate the probabilities of (i), (ii), and (iii) and add up.

To calculate say Case (ii), find the probability of $4$ orders (this comes from the Poisson) and then the probability of $1$ double and $3$ singles, given $4$ orders.

The conditional probability of $1$ double, $3$ singles given there are $4$ orders is a binomial distribution problem. We get $\binom{4}{1}(0.7)^1(0.3)^3$. For the probability of (ii), multiply by $e^{-5}\frac{5^4}{4!}$.