Question

A raffle is held where winners have the option to keep or donate the prize money.

Of the people who enter the raffle, only 16% of people win. Of the winners, 60% choose to donate the prize money.

What is the probability that someone will win the raffle and donate the prize money?

Answer 1

To find the probability that someone will win the raffle and choose to donate the prize money, we can use the following information:

1. The probability of winning the raffle: \( P(\text{Win}) = 0.16 \) (16%)
2. The probability of donating the prize money given that they have won: \( P(\text{Donate} | \text{Win}) = 0.60 \) (60%)

We want to find the joint probability \( P(\text{Win} \cap \text{Donate}) \), which can be calculated using the formula for conditional probability:

\[
P(\text{Win} \cap \text{Donate}) = P(\text{Win}) \times P(\text{Donate} | \text{Win})
\]

Substituting the known values:

\[
P(\text{Win} \cap \text{Donate}) = 0.16 \times 0.60
\]

Calculating this gives:

\[
P(\text{Win} \cap \text{Donate}) = 0.096
\]

Thus, the probability that someone will win the raffle and donate the prize money is **0.096**, or **9.6%**.