BrentGMATPrepNow wrote:
A box contains 7 balls, and each ball is exactly 1 color (i.e., there are no multi-colored balls). If two balls are randomly selected without replacement, what is the probability that both selected balls will be blue?
(1) The probability is greater than 0.5 that both selected balls will be yellow.
(2) The probability is less than 0.25 that the first ball selected will be blue.
Target question: What is the probability that both selected balls will be blue? Statement 1: The probability is greater than 0.5 that both selected balls will be yellow. Let's test some possible case:
case i: All 7 balls are yellow. In this case, p(both selected balls are yellow) = 1, which is greater than 0.5.
case ii: 6 of the 7 balls are yellow. In this case, p(both selected balls are yellow) = 6/7 x 5/6 = 5/7 ≈ 0.71, which is greater than 0.5.
case iii: 5 of the 7 balls are yellow. In this case, p(both selected balls are yellow) = 5/7 x 4/6 = 20/42, which is LESS THAN 0.5
Since we are told p(both selected balls are yellow) > 0.5, then there are EITHER 6 yellow balls OR 7 yellow balls in the box.
This means there is AT MOST 1 blue ball in the box.
If there is AT MOST 1 blue ball in the box, then
p(both selected balls are blue) = 0Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The probability is less than 0.25 that the first ball selected will be blue.Let's test some possible case:
case i: None of the 7 balls are blue. In this case, p(first selected ball is blue) = 0, which is less than 0.25.
case ii: 1 of the 7 balls is blue. In this case, p(first selected ball is blue) = 1/7 = 0.14, which is less than 0.25.
case iii: 2 of the 7 balls are blue. In this case, p(first selected ball is blue) = 2/7 = 0.28, which is GREATER THAN 0.25.
So, there are EITHER 0 blue balls in a box OR 1 blue ball in the box.
In both possible cases,
p(both selected balls are blue) = 0Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D