Question

jason bought 10 of the 30 raffle tickets for a drawing. assuming that he chooses the winning ticket each time, what is the probability that jason will win all 3 of the prizes if once a raffle ticket wins a prize, the ticket is thrown away?
\\(\frac{6}{203}\\)
\\(\frac{1}{27}\\)
\\(\frac{3}{29}\\)
\\(\frac{1}{9}\\)

Explanation:

Step1: Probability for first win

Jason has 10 tickets out of 30. So the probability of winning the first prize is $\frac{10}{30}=\frac{1}{3}$.

Step2: Probability for second win

After winning the first prize, the ticket is thrown away. So now there are 9 of Jason's tickets left and total 29 tickets. Probability of winning second prize is $\frac{9}{29}$.

Step3: Probability for third win

After winning the second prize, there are 8 of Jason's tickets left and total 28 tickets. Probability of winning third prize is $\frac{8}{28}=\frac{2}{7}$.

Step4: Multiply the probabilities

To find the probability of winning all three prizes, we multiply the probabilities of each event: $\frac{1}{3}\times\frac{9}{29}\times\frac{2}{7}=\frac{1\times9\times2}{3\times29\times7}=\frac{18}{609}=\frac{6}{203}$.

Answer:

$\frac{6}{203}$ (corresponding to the first option)