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? StartFraction 6 over 203 EndFraction StartFraction 1 over 27 EndFraction StartFraction 3 over 29 EndFraction StartFraction 1 over 9 EndFraction

Answer 1

Given:

Total of raffle tickets = 30

Number of tickets Jason bought = 10

Number of prizes = 3

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.

Solution:

Total of raffle tickets = 30

Number of prizes = 3

So, number of total outcomes is

$n(S)=^{30}C_3$

Number of tickets Jason bought = 10

So, number of favorable outcomes is

$n(A)=^{10}C_3$

Now,

$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$\text{Probability}=\dfrac{n(A)}{n(S)}$

$\text{Probability}=\dfrac{^{10}C_3}{^{30}C_3}$

$\text{Probability}=\dfrac{\dfrac{10!}{(10-3)!3!}}{\dfrac{30!}{(30-3)!3!}}$

$\text{Probability}=\dfrac{10\times 9\times 8\times 7!}{7!3!}\times\dfrac{27!3!}{30\times 29\times 28\times 27!}$

$\text{Probability}=\dfrac{10\times 9\times 8}{30\times 29\times 28}$

$\text{Probability}=\dfrac{6}{203}$

Therefore, the correct option is A.