If a person purchases 15 of the 3,000 tickets sold in a raffle that aw

Probability for him to win = 15/3000 = 1/200

Probability for him to NOT win = 1-1/200 = 199/200

Answer: Option D

Let's use the complement: P(Event A happening) = 1 - P(Event A not happening)

Given: P(person wins) \(= \frac{15}{3000}\)

So, P(person does NOT win) \(= 1 - \frac{15}{3000}\)

Simplify to get: P(person does NOT win) \(= 1 - \frac{1}{200}\)

Rewrite with common denominator to get: P(person does NOT win) \(= \frac{200}{200} - \frac{1}{200} = \frac{199}{200}\)

Answer: D

Cheers,
Brent

Solution:

The probability of not winning is (3,000 - 15) / 3,000 = 2,985 / 3,000 = 597 / 600 = 199 / 200.

Alternate solution:

The probability of winning is 15/3,000 = 1/200; thus, the probability of not winning is 1 - 1/200 = 199/200.

Answer: D
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GMATNinja, Bunuel, can you please explain what does it mean 3000 tickets sold in a raffle that award one winning prize?
I mistakenly assumed that all tickets must produce winning outcome.

A raffle is basically a form of gambling: in this example, there are 3000 tickets (in, say, a large bucket), and one ticket will be randomly selected from the bucket. The person who owns that ticket wins the prize. The other 2999 tickets will make their owners slightly sad.

Does that help?
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GMATNinja, does it mean that individual will not win the prize as a result of selecting other 2999 tickets?

Yes, exactly. Whoever has the single "winning" ticket wins the single prize. The other ticket holders (the people holding the 2999 non-winning tickets) get nothing.

If you search for "Double Ticket Roll" on the internet, you'll see images of what these raffle tickets often look like. For each ticket number (say, 1-3000), there are two tickets: one that's given to the contestant and one that's kept by whoever is selling the tickets (sort of like a "receipt" for that particular number). So if 3000 tickets are sold, the seller will have 3000 "receipt" tickets. The seller puts those 3000 "receipt" tickets in a bucket and selects only one to generate the winning number. One contestant will have the corresponding ticket for that number, and that contestant will win the prize. The people holding tickets corresponding to the other 2999 numbers don't get anything.

Gambling is awesome.
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