Jason bought 10 of the 30 raffle tickets for a drawing. What is the probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away?
To calculate the probability of Jason winning all 3 prizes, we need to determine the probability of winning each individual prize and then multiply them together.
First, let's calculate the probability of winning the first prize. Jason bought 10 out of 30 tickets, so his chance of winning the first prize is 10/30.
Once the first prize is won, one winning ticket is removed from the pool, leaving 9 winning tickets out of 29. Therefore, the probability of Jason winning the second prize is 9/29.
Similarly, after the second prize is won, there are now 8 winning tickets out of 28 left. Therefore, the probability of Jason winning the third prize is 8/28.
To find the probability of all three events happening (Jason winning all the prizes), we multiply the probabilities together:
P(Jason winning all 3 prizes) = (10/30) * (9/29) * (8/28)
Simplifying the fraction, we get:
P(Jason winning all 3 prizes) = (1/3) * (3/10) * (2/7)
Multiplying the numerators (1 * 3 * 2) and the denominators (3 * 10 * 7), we get:
P(Jason winning all 3 prizes) = 6/210
Simplifying the fraction, the probability of Jason winning all 3 prizes is 1/35 or approximately 0.0286, which is approximately 2.86%.
To find the probability of Jason winning all 3 prizes, we need to calculate the probability of winning one prize and multiply it by the probability of winning the next prize and so on.
Let's break down the problem into steps:
Step 1: Calculate the probability of Jason winning the first prize.
Since Jason bought 10 tickets out of a total of 30 tickets, the probability of winning the first prize is 10/30.
Step 2: After winning the first prize, the winning ticket is thrown away, reducing the total number of tickets for the second prize to 29.
Jason now has 9 tickets left out of 29, so the probability of winning the second prize is 9/29.
Step 3: Similarly, after winning the second prize, the winning ticket is thrown away, reducing the total number of tickets for the third prize to 28.
Jason now has 8 tickets left out of 28, so the probability of winning the third prize is 8/28.
Finally, we can calculate the probability of Jason winning all 3 prizes by multiplying the probabilities from each step:
Probability of winning all 3 prizes = (10/30) * (9/29) * (8/28)
Now we can simplify this expression to find the final answer.