One of four different prizes was randomly put into each box of a cereal. If a family decided to buy this cereal until it obtained at least one of each of the four different prizes, what is the expected number of boxes of cereal that must be purchased?
For this question, I don't understand why it can be thought of as a model of negative binomial distribution with the expected value of $E(x)=$ $\frac {1}{p}$
Best Answer
Now for obtaining prize 1
$\sum_{r=1}^{\infty} r\frac{3^{r-1}}{4^r} =4$
If i buy 4 boxes it is expected i will get prize 1. Same could be said about other prizes. Expected value is 4.(Caution you should not add 4 '4' times , because getting prize 2 is completely independent of prize 1)
If they buy 4 packs , it is expected that they get each reward .