If a person purchases 15 of the 3,000 tickets sold in a raffle that awards one prize, what is the probability that...

[BTGmoderatorLU]

Source: GMAT Prep

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

[Scott@TargetTestPrep]

Source: GMAT Prep

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

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

[Brent@GMATPrepNow]

Source: GMAT Prep

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

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

Given: P(person wins) [m]= [fraction]15/3000[/fraction][/m]

So, P(person does NOT win) [m]= 1 - [fraction]15/3000[/fraction][/m]

Simplify to get: P(person does NOT win) [m]= 1 - [fraction]1/200[/fraction][/m]

Rewrite with common denominator to get: P(person does NOT win) [m]= [fraction]200/200[/fraction] - [fraction]1/200[/fraction] = [fraction]199/200[/fraction][/m]

Answer: D

Cheers,
Brent