Odds to Win Raffle

Question

What are the odds of winning a raffle that sells 10 tickets with four (4) winners? Winning tickets are put back in the raffle for future drawings. I purchase three (3) tickets. What are my odds to win 1 time, 2 times or 3 times?

Answer 1

To calculate the odds of winning a raffle, you can use a probability approach. In this scenario, there are 10 tickets, 4 of which are winners, and the winning tickets are put back in the raffle for future drawings. You purchase 3 tickets. Let's calculate the odds of winning 1, 2, or 3 times.

To find the odds of winning a specific number of times, you can use combinations and the binomial probability formula.

The probability of winning 1 time:

P(1 win) = C(3, 1) * P(win) * P(lose)^2

Where:

- C(3, 1) is the number of ways to choose 1 winning ticket out of 3, which is equal to 3.

- P(win) is the probability of winning on a single ticket, which is 4/10.

- P(lose) is the probability of losing on a single ticket, which is 6/10.

P(1 win) = 3 * (4/10) * (6/10)^2 = 0.432

So, the odds of winning 1 time are approximately 43.2%.

The probability of winning 2 times:

P(2 wins) = C(3, 2) * P(win)^2 * P(lose)

Where:

- C(3, 2) is the number of ways to choose 2 winning tickets out of 3, which is equal to 3.

- P(win) is the probability of winning on a single ticket, which is 4/10.

- P(lose) is the probability of losing on a single ticket, which is 6/10.

P(2 wins) = 3 * (4/10)^2 * (6/10) = 0.288

So, the odds of winning 2 times are approximately 28.8%.

The probability of winning 3 times:

P(3 wins) = C(3, 3) * P(win)^3

Where:

- C(3, 3) is the number of ways to choose 3 winning tickets out of 3, which is equal to 1.

- P(win) is the probability of winning on a single ticket, which is 4/10.

P(3 wins) = 1 * (4/10)^3 = 0.064

So, the odds of winning 3 times are approximately 6.4%.

To calculate your overall odds of winning at least once, you can add the probabilities of winning 1 time, 2 times, and 3 times:

Overall odds = P(1 win) + P(2 wins) + P(3 wins)

Overall odds = 0.432 + 0.288 + 0.064 = 0.784

So, your odds of winning at least once are approximately 78.4%.

I hope this will help. I am happy to tutor you on any other questions you may have; please feel free to shoot me a message!