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25 Jan 2026, 22:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
37% (02:02) correct
63%
(02:08)
wrong
based on 68
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Lily has only red and blue balls in a jar. If she removes three balls, is the probability of getting all red balls greater than the probability of getting at least one blue ball?
(1) The number of red balls is more than three times the number of blue balls.
(2) Less than 1 / 4 th of the balls in the jar are blue.
(1) The number of red balls is more than three times the number of blue balls.
(2) Less than 1 / 4 th of the balls in the jar are blue.
26 Jan 2026, 00:30
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Lily has only red and blue balls in a jar. If she removes three balls, is the probability of getting all red balls greater than the probability of getting at least one blue ball?
(1) The number of red balls is more than three times the number of blue balls.
(2) Less than 1 / 4 th of the balls in the jar are blue.
Let the number of Red balls in the jar be 'R', and the number of Blue balls in the jar be 'B'. We need to determine if P(All 3 Red) > P(Atleast 1 Blue) OR P(All 3 Red) > 1-P(All 3 Red). Hence, effectively, we need to check if P(All 3 Red) > 1/2.
Now, let's look at each statement individually and then at both of them together (if required):
Statement 1: The number of red balls is more than three times the number of blue balls.
Given: R > 3B
The easiest way to check this statement would be to assume values in order to arrive at the answer.
Let's assume B = 1 and R = 6:
P(All 3 Red) = 6/7 * 5/6 * 4/5 = 4/7, which is lesser than 1/2
Thus, the answer should be NO according to these values. However, we also need to check if the answer can be YES in any case, as we need a unique answer to be completely sure.
Now, let's assume B = 2 and R = 9:
P(All 3 Red) = 9/11 * 8/10 * 7/9 = 28/55, which is greater than 1/2
Thus, the answer should be YES according to this set of values.
As we aren't able to arrive at a unique answer using Statement 1 alone, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Less than 1 / 4 th of the balls in the jar are blue.
Given: B/(R+B) < 1/4 => R > 3B, which is basically the same information that has been provided as part of Statement 1. Hence, we cannot arrive at a unique answer using Statement 2 alone too.
As both the statements convey the same information, both are insufficient.
Hence, the correct answer is Option E - Neither statement alone nor together is sufficient.
Hope this helps!
(1) The number of red balls is more than three times the number of blue balls.
(2) Less than 1 / 4 th of the balls in the jar are blue.
Let the number of Red balls in the jar be 'R', and the number of Blue balls in the jar be 'B'. We need to determine if P(All 3 Red) > P(Atleast 1 Blue) OR P(All 3 Red) > 1-P(All 3 Red). Hence, effectively, we need to check if P(All 3 Red) > 1/2.
Now, let's look at each statement individually and then at both of them together (if required):
Statement 1: The number of red balls is more than three times the number of blue balls.
Given: R > 3B
The easiest way to check this statement would be to assume values in order to arrive at the answer.
Let's assume B = 1 and R = 6:
P(All 3 Red) = 6/7 * 5/6 * 4/5 = 4/7, which is lesser than 1/2
Thus, the answer should be NO according to these values. However, we also need to check if the answer can be YES in any case, as we need a unique answer to be completely sure.
Now, let's assume B = 2 and R = 9:
P(All 3 Red) = 9/11 * 8/10 * 7/9 = 28/55, which is greater than 1/2
Thus, the answer should be YES according to this set of values.
As we aren't able to arrive at a unique answer using Statement 1 alone, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Less than 1 / 4 th of the balls in the jar are blue.
Given: B/(R+B) < 1/4 => R > 3B, which is basically the same information that has been provided as part of Statement 1. Hence, we cannot arrive at a unique answer using Statement 2 alone too.
As both the statements convey the same information, both are insufficient.
Hence, the correct answer is Option E - Neither statement alone nor together is sufficient.
Hope this helps!
26 Jan 2026, 22:29
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ExpertsGlobal5
Lilly has red and blue balls only in a jar.
She removes three balls out of the jar.
We need to find: Probabilty of Red > Probability of Atleast 1 Blue
Probability of ATLEAST ONE blue ball = 1- ( Probabilty of all Red)
Thus, Probability of Red ball > 1- ( Probabilty of all Red)
2* Probability of Red ball > 1
Is Probability of Red ball > (1/2)?
Statement 1:
The number of red balls is more than three times the number of blue balls.
R > 3 B
This is an open equation. When B =1 and R can take any positive integers greater than 4. Say, 4,5,6,..10,1000,1000000 and so on.
For values which are less R=4 and B =1 , total =5
The probability of taking three red balls = (4/5)*(3/4)*(2/3) = (2/5)=0.4
But, if we increase the value of R =19 and B=1, total 20
The probability of taking three red balls = (19/20)*(18/19)*(17/18) = (17/20)=0.85
Two different values arise. Hence, Insufficient
Statement 2:
(2) Less than 1 / 4 th of the balls in the jar are blue.
B < (1/4)* (R+B)
solving we get R> 3B
This is same as statement 1. Hence, Insufficient
Combining both statements 1 and 2, we get
R> 3B
Hence, Insufficient
Option E
