Data Sufficiency

BTGModeratorVI wrote: ↑

Sun Aug 02, 2020 6:55 am

Dennis cooks dishes in three colors - red, white and yellow. If Norman, the renowned restaurant critic, selects one dish randomly, what is the probability that the selected dish will be either white or yellow?

(1) The probability that the dish will be yellow is 1/5

(2) The probability that the dish will be red is 1/3

Answer: B
Source: Economist GMAT

Given: Dennis cooks dishes in three colors - red, white and yellow.

Target question: P(selected dish is white or yellow) = ?

Statement 1: The probability that the dish will be yellow is 1/5
Since we aren't given any information about the probability that the dish is white, there is no way to answer the target question with certainty.
Statement 1 is NOT SUFFICIENT

Statement 2: The probability that the dish will be red is 1/3
The key concept here involves complements:
That is, P(Event A happening) = 1 - P(Event A not happening)
So, for statement 2, we can write: P(dish is red) = 1 - P(dish is NOT red)
Substitute values to get: 1/3 = 1 - P(dish is NOT red)
Solve this equation to get: P(dish is NOT red) = 2/3
How does this help us?
Well, what does it mean to get a dish that is NOT red?
It means the dish is either white or yellow.
So, P(dish is NOT red) = P(dish is white or yellow) = 2/3
The answer to the target question is P(selected dish is white or yellow) = 2/3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent