What is the probability of winning with 5 tickets?

[Qube]

Homework Statement

A woman has 5 tickets for a contest. There are 1,000 tickets total. Two tickets out of those 1,000 tickets will deem people as winners and they will receive prizes. What is the probability that the woman with the 5 tickets will win a prize?

Homework Equations

Could you find the complement of the event and subtract the probability of the complement from 1?

The Attempt at a Solution

Complement = P(Not getting a winning ticket)

998 non-winning tickets. Probabilities:

1/998 * 1/997 * 1/996 * 1/995 * 1/994 = P(Not getting a winning ticket)

Subtract the above from one.

However, the fact she has five tickets complicates matters; what do I do?

 

[vela]

You already took into account that she has five tickets when calculating the probability she wouldn't have a winning ticket.

 

[Qube]

So I can just subtract the complement from 1?

 

[vela]

Yup.

 

[vela]

Oops, you calculated the probability incorrectly. She has 998 ways out of 1000 to pull the first non-winning ticket, not 1 out of 998, and so on.

 

[Qube]

Oops, you calculated the probability incorrectly. She has 998 ways out of 1000 to pull the first non-winning ticket, not 1 out of 998, and so on.

You're right. I actually calculated it correctly before I transcribed my work to PF. It's 998/1000 * 997/999 * 996/998 ...