A box has at least one ball of each of the co...
A box has at least one ball of each of the colors red, green, and blue and no balls of any other color. If one ball is drawn randomly from the box, is the probability that the drawn ball is red same as the probability that the drawn ball is blue but NOT the same as the probability that the drawn ball is green?
(1) There are 5 balls in the box.
(2) The number of green balls is greater than the number of blue balls.
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
A box has at least one ball of each of the colors red, green, and blue...
We are given that the box has balls of three different colors - red, blue and green, and the number of balls of each color is at least one in count. Thus, the minimum number of balls in the box = 3.
Let's understand what the question asks.
When one ball is drawn,
Is "(Probability of drawing a red ball) = (Probability of drawing a blue ball) ≠ (Probability of drawing a green ball)"
Say, the probability of drawing a red ball = p(r); the probability of drawing a blue ball = p(b); and the probability of drawing a green ball = p(g).
Is p(r) = p(b) ≠ p(g)?
So, the question boils down to:
"Does the box has the number of red color balls equal to the number of blue color balls but NOT equal to the number of green color balls?"
Statement 1:
There are 5 balls in the box.
Let's distribute them in three color balls such that we have at least one ball of each color.
Scenario 1: Red color: 1 ball; Blue color: 1 ball; and Green color: 3 balls.
We have the number of red color balls equal to the number of blue color balls, and NOT equal to the number of green color balls; the answer is Yes.
Scenario 2: Red color: 2 ball; Blue color: 1 ball; and Green color: 2 balls.
We have the number of red color balls NOT equal to the number of blue color balls, but equal to the number of green color balls; the answer is No.
Note: Other scenarios are possible too but we do not need to consider them all because from just two scenarios, we can already see that Statement 1 is not sufficient for a unique answer.
Statement 2:
Only with this information, we can decide that the probability that the drawn ball is green is NOT equal to the probability that the drawn ball is blue; however, we have no clue about the number of red balls; number of red balls may or may not be equal to number of blue balls. Insufficient.
Statement 1 & 2:
Both the scenarios discussed in Statement 1 are applicable here too. Insufficient.
Had Statement 2 been, "The number of green color balls is greater than the number of blue balls and greater than the number of red balls," Scenario 2 would not have been applicable here, thus the answer would then be C.
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