# Lottery probability question

#### juliej

##### New member
Need help with a lottery problem with 2 questions:
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.)
1. What is the probability of winning some cash?
2. What is the probability of winning cash or a free ticket?

#### pka

##### Elite Member
Need help with a lottery problem with 2 questions:
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.
1)What is the probability of winning some cash?
2)What is the probability of winning cash or a free ticket?
Because these events are mutually disjoint and independent the probabilities are additive.
So apply that idea to both of these.

#### juliej

##### New member
Because these events are mutually disjoint and independent the probabilities are additive.
So apply that idea to both of these.
Thanks! Sorry about that but I was really stuck on this one when I posted.
I am assuming what you said though I wasn't sure if winning 5 included winning 3 and 4.
So I was thinking the P(winning some cash) = 1/103 + 1/3387 + 1/575,757
and P(winning cash or a free ticket) = 1/103 + 1/3387 + 1/575,757 + 1/10.
Please give me some input if you think this is not correct. Much appreciated!

#### Jomo

##### Elite Member
I am assuming what you said though I wasn't sure if winning 5 included winning 3 and 4.
So I was thinking the P(winning some cash) = 1/103 + 1/3387 + 1/575,757
I thought the same thing until I looked at the numbers. Do you think that 1/103 + 1/3387 < 1/575,757?

#### pka

##### Elite Member
Thanks! Sorry about that but I was really stuck on this one when I posted.
I am assuming what you said though I wasn't sure if winning 5 included winning 3 and 4.
So I was thinking the P(winning some cash) = 1/103 + 1/3387 + 1/575,757
and P(winning cash or a free ticket) = 1/103 + 1/3387 + 1/575,757 + 1/10.
Please give me some input if you think this is not correct. Much appreciated!
I am read this as if one can only one the four possibilities on any the five numbers on one ticket.
So that is the sum of the four probabilities. that is winning exactly once.