We start with 5000 forints in our pocket to buy gifts. We enter three stores. In each store, we like a gift item, which we will buy if we can afford it. The prices of the items in each store, independently of each other, are 1000, 1500, or 2000 Ft with a probability of $\frac{1}{3}$. What is the probability that we will manage to buy three gift items and still have money left?
Solution. Since gift items occur with the same probability in every store, we have a total of $3^{3}=27$ possibilities for shopping.

During shopping, we can spend at least 3000 and at most 4500 forints, as we have a total of 5000 forints and we still need to have some money left. Let's calculate how many possibilities there are where we would spend more than 4500 forints.

If we bought the most expensive, 2000 forint gift in every store, we would pay a total of 6000 forints. This is 1 possibility.

We would pay 5500 forints if we bought 2 items for 2000 forints and 1 item for 1500 forints. We could do this in three ways: either in the first, second, or third store. This adds up to 3 new possibilities.

We pay 5000 forints when we choose a 1000 forint item along with 2 items for 2000 forints. Similarly to the previous case, this gives us 3 more possibilities. We also pay 5000 forints when we choose a 2000 forint item along with 2 items for 1500 forints. This also gives us 3 possibilities.

With this, we have listed all the unfavorable cases. Their number is 10, so the number of favorable cases is $27-10=17$, and the probability we are looking for is $\frac{17}{27} \approx 0.63$.