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

The correct answer is A. 6/203

Answer 2

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}=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}`

`\text{Probability}=(n(A))/(n(S))`

`\text{Probability}=(^(10)C_3)/(^(30)C_3)`

`\text{Probability}=((10!)/((10-3)!3!))/((30!)/((30-3)!3!))`

`\text{Probability}=(10* 9* 8* 7!)/(7!3!)*(27!3!)/(30* 29* 28* 27!)`

`\text{Probability}=(10* 9* 8)/(30* 29* 28)`

`\text{Probability}=(6)/(203)`

Therefore, the correct option is A.