# Thread: Lottery Game Chance!! a little insight

1. ## Lottery Game Chance!! a little insight

Problem: Suppose in a lottery game the chance of winning is 15%. If a person purchases 10 tickets, what is the probability of 3 winning tickets?

I was using the binomial distribution method, where p(win) = .15 , n = 10, x = 3

and got 0.1298 , does this sound right? What approach should I be using?

2. ## That's right

Hi. Your logic is fine. You have 10 independent trials and at each trial the event A={The ticket wins} occurs with the same probability. This is called a Bernouli scheme and is solved with binomial distribution. You have 3 tickets.
Pr("the ticket wins")=10C3*(0.15)^3*(0.85)^7.

3. Originally Posted by isuckatprobability
Problem: Suppose in a lottery game the chance of winning is 15%. If a person purchases 10 tickets, what is the probability of 3 winning tickets?

I was using the binomial distribution method, where p(win) = .15 , n = 10, x = 3

and got 0.1298 , does this sound right? What approach should I be using?
You are correct provided that you want the probability of getting EXACTLY 3 winning tickets.

If you are actually interested in the probability of getting AT LEAST 3 winning tickets then you will need to find the probabilities of getting exactly 3, 4, 5, ..., 10 winning tickets and add them up. Or you can add up the probabilities of getting 0, 1, or 2 winning tickets and subtract from 1.