Question

A local farming club is selling raffle tickets for $15 each for a chance to win a milking cow. They will sell $6,000 worth of raffle tickets to fund their next project. If someone buys 2 tickets, what is the probability that that person will win the milking cow?

Answer 1

To find the probability that a person who buys 2 raffle tickets will win the milking cow, we first need to determine the total number of raffle tickets sold.

Since the farming club will sell $6,000 worth of raffle tickets at $15 each, we calculate the total number of tickets sold as follows:

\[
\text{Total tickets sold} = \frac{\text{Total money from tickets}}{\text{Price per ticket}} = \frac{6000}{15} = 400
\]

Next, if a person buys 2 tickets, we need to find the probability that at least one of their tickets wins. The total number of favorable outcomes (winning tickets) when buying 2 tickets is 2 (since they have 2 tickets).

Now, the probability that a person does not win (all their tickets lose) can be calculated by using the total number of tickets:

1. The total number of tickets is 400.
2. The number of losing tickets is \(400 - 1 = 399\) (since there is only 1 winning ticket).

Now we calculate the probability that both tickets purchased by the person are losing tickets:

\[
P(\text{losing with 2 tickets}) = \frac{399}{400} \times \frac{398}{399} = \frac{398}{400}
\]

Therefore, the probability that the person wins with at least one of their two tickets is:

\[
P(\text{winning with at least 1 ticket}) = 1 - P(\text{losing with both tickets}) = 1 - \frac{398}{400} = \frac{2}{400} = \frac{1}{200}
\]

Thus, the probability that a person who buys 2 tickets will win the milking cow is:

\[
\boxed{\frac{1}{200}}
\]