Probablity of Winning The probability of winning a free ticket (for matching 2 of 5 numbers) in a particular state lottery is 1 in 10; the probability of winning cash for matching 3 of 5 numbers is 1 in 103; and the probability of winning cash for matching 4 of 5 numbers is 1 in 3387. The probability of winning cash for choosing 5 of 5 winning numbers is 1 in 575,757. (The amount of cash won depends on how many winners split the prize.) a)What is the probability of winning some cash? b)What is the probability of winning cash or a free ticket? Thanks for any help you can give. I am helping a student with this one and it has me stumped. I assume the P(winning some cash) = P(matching 3 or 4 or 5 numbers). Do you just then just add the probability for those 3? Or is it 1 - the sum of probability for those 3? And for P(winning cash or a free ticket) do you just add the probability for all that's given? Or is it 1 - all those probabilities that are given?

Presumably the probabilities you are given are disjoint. The $1$ in $10$ for getting a free ticket does not include the chance you match $3$ or more numbers. In that case you can just add the probabilities.

If they are not disjoint, the chance of getting $4$ or $5$ is included in the chance of $3$, so you can just use the chance of $3$ as the chance of getting cash. Similarly the chance of winning anything would be the chance of getting $2$.