Question

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?

Answer 1

10/30) x (9/29) x (8/28)  =  720 / 24,360

                                                             =  6 / 203  =  2.96 percent (rounded)   

Answer 2

Answer:  The required probability that Jason wins all the 3 prizes is 2.96%.

Step-by-step explanation:  Given that Jason bought 10 of the 30 raffle tickets for a drawing.

We are to find the probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize it is thrown away.

Let S denote the sample space for the experiment of drawing 3 tickets from 30 raffle tickets and A denote the event that Jason wins all the 3 prizes.

Since a raffle ticket is thrown away once it wins a prize, so

$n(S)=^{30}P_3=\dfrac{30!}{(30-3)}=\dfrac{30!}{27!}=\dfrac{30\times29\times28\times27!}{27!}=24360,\\\\\\n(A)=^{10}P_3=\dfrac{10!}{(10-3)!}=\dfrac{10!}{7!}=\dfrac{10\times9\times8\times7!}{7!}=720.$

Therefore, the probability of event A is given by

$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{720}{24360}=0.029955=2.96\%.$

Thus, the required probability that Jason wins all the 3 prizes is 2.96%.