If a person purchases 15 of the 3,000 tickets sold in a raffle that awards one prize, what is the probability that this person will not win?

A. 0
B. 1/200
C. 1/2
D. 199/200
E. 1

Two solutions, same answer:

(1) Pure method:

P = P(winning ) = 15/3000 = 5/1000 = 1/200
P' = (P of not winning) = 1 - P = 1 - 1/200 = 199/200

(2) Looking at the given answers:

A. 0 - It is not impossible to lose!
B. 1/200 - A disproportionately small value!
C. 1/2 - It's clearly not an even chance!
D. 199/200 - is a reasonable figure
E. 1 - It is not certain to lose!

If a person purchases 15 of the 3,000 tickets sold in a raffle that awards one prize, what is the probability that this person will not win?

A. 0
B. 1/200
C. 1/2
D. 199/200
E. 1

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer.

I know that the probability that this person will win is 15/3000, but how can I determine the probability that this person will not win?. I need your help. Thanks.

Hi swerve,
Let's take a look at your question.

We know that we can find the probability of an event by dividing the number of successful outcomes divided by the total number of outcomes.
Number of tickets purchased by a person = 15
Total number of tickets = 3000

We will first find the probability of winning.
$$P\left(\text{The person will win}\right)=\frac{15}{3000}=\frac{1}{200}$$

Now, we can find the probability that the person will not win just by subtracting the above probability from 1.
$$P\left(\text{The person will not Win}\right)=1-\frac{1}{200}=\frac{200-1}{200}=\frac{199}{200}$$

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.