# Thread: Lottery Problem, Help!! life or death question

1. ## Lottery Problem, Help!! life or death question

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. 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 should let $\displaystyle X$ be "the number of tickets that win", so:

$\displaystyle X = Bin(10, 0.15)$

Then find $\displaystyle P(X = 3)$:

$\displaystyle P(X = 3) = P(X \leq 3) - P(X \leq 2)$
$\displaystyle P(X = 3) = .95 - .82$
$\displaystyle P(X = 3) = .13$

So yes, it sounds right.