A box has at least one ball of each of the colors red, green, and blue

Question

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.

(1) There are 5 balls in the box.

(2) The number of green balls is greater than the number of blue balls.

RayanCHB · Answer

Statement (1) : tells us all three probabilities can't be equal. Not sufficient.
Statement (2) : The likelihood of pulling green balls is greater than that of pulling blue balls. No indication about red balls though. Not sufficient

Statements (1) and (2) : we could have 1 red 1 blue and 3 green (total of 5 with a greater green > blue) which gives
Pred = Pblue = 1/5 and Pgreen = 3/5.
Or we could have 2 red 1 blue and 2 green (total of 5 with a greater green > blue) which gives
Pred = Pgreen = 2/5 and Pblue = 1/5.

Ans = E

itsgauravjain · Answer

Where are all the options?

Bunuel · Answer

Hi,

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

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 to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post  ALL YOU NEED FOR QUANT .

Hope this helps.

LILICHKA · Answer

Strange! I think A must be enough:
in how many ways can 5 balls be assigned to 3 colors, given there is at least one ball of each color?
it's either 1-2-2 (and another 2 permutations of "1") or 1-1-3 (and another 2 permutations of "3"), giving us 6 altogether
How many options of these six provide, that red (let's say that's the first number) equal blue (let's say that's the second number), and doesn't equal the greed (let's say it's the third number)
only two of them: 1-1-3 and 2-2-1. so it's 1/3 and it's calculatable.
UPD I think I misread the qn. They aren't asking, what's the probability, they are asking, if the three are specially interrelateD:)

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are asked if  P(R) = P(B) ≠ P(G)  or not 
 This will be true if  number of red balls (r) = number of blue balls (b) ≠ number of green balls (g)  in the box

Statement 1:   There are 5 balls in the box 
  Knowing the total number of balls is not going to tell us if  P(R) = P(B) ≠ P(G)  or not 
 If r = 1, b = 1 and g = 3, then  P(R) = P(B) ≠ P(G)  is true 
 However, if r = 2, b = 1 and g = 2, then  P(R) = P(B) ≠ P(G)  is not true 
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:   The number of green balls is greater than the number of blue balls 
  If r = 1, b = 1 and g = 3, then  P(R) = P(B) ≠ P(G)  is true 
 However, if r = 2, b = 1 and g = 2, then  P(R) = P(B) ≠ P(G)  is not true 
 Thus,  statement 2 alone is also not sufficient

Combining:   
  If r = 1, b = 1 and g = 3, then  P(R) = P(B) ≠ P(G)  is true
 However, if r = 2, b = 1 and g = 2, then  P(R) = P(B) ≠ P(G)  is not true

Hence the right answer is    Option E

bumpbot · Answer

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A box has at least one ball of each of the colors red, green, and blue

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GMAT Data Sufficiency (DS) Questions

A box has at least one ball of each of the colors red, green, and blue

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