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
[tex]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.[/tex]
Therefore, the probability of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{720}{24360}=0.029955=2.96\%.[/tex]
Thus, the required probability that Jason wins all the 3 prizes is 2.96%.
