Lily has only red and blue balls in a jar. If she removes three balls

Question

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.

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Nielgmat · Answer

Is P(all 3 red) > P (atleast 1 blue) ?

1. The number of red balls is more than three times the number of blue balls.

assume red ball = 10, blue = 3
P(all3 red) = 10C3/ 13C3 = 120/286
P(atleast 1 blue) = 1 - (all 3 red)
 = 1- 120/286
 = 166/286

so ans is YES, hold on to A.

2. Less than 1/4 th of the balls in the jar are blue.

assume red ball = 10, blue = 2

similar calculations as above, ans is yes again, eliminate A, choose D.
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Not sure if my process and answer is correct...experts pls help.
Also took more than 3 mins,..i am sure it can be done faster..

prakashb2497 · Answer

Can you help with a solution for this?

Bunuel   chetan2u

chetan2u · Answer

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?

We require to know the number of red and blue balls. Also the two probabilities P(all red) and P(at least one blue) will add up to 1.
So knowing anyone of the P to be greater than 1/2 will give a definite answer.

(1) The number of red balls is more than three times the number of blue balls.
 A wide range - In 1000 balls, red could be 751 to 999.  
Red balls in very high proportion will give YES: 
Say 1000 balls out of which 999 are red and one blue - P(all 3 red) = 999C3/1000C3 = 997/1000 and P(at least one Blue) = 999C2*1C1/1000C3 = 3/1000
Exactly 3 times will give a NO:
Say 5 balls out of which 4 are red - P(all 3 red) = 4C3/5C3 = 2/5 and P(at least one Blue) = 4C2*1C1/5C3 = 3/5 
Insufficient

(2) Less than (1)/(4) th of the balls in the jar are blue.
 This again leaves a wide range in front of us and blue can have varying values. For example out of 1000 balls, blue could vary from 1 to 249. 
Red balls in very high proportion will give YES: 
Say 1000 balls out of which 999 are red and one blue - P(all 3 red) = 999C3/1000C3 = 997/1000 and P(at least one Blue) = 999C2*1C1/1000C3 = 3/1000
Red balls in not a very high proportion will give a NO:
Say 5 balls out of which 4 are red - P(all 3 red) = 4C3/5C3 = 2/5 and P(at least one Blue) = 4C2*1C1/5C3 = 3/5 
Insufficient

Combined
Nothing new

E

shivani1351 · Answer

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!

Dereno · Answer

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

ExpertsGlobal5 · Answer

Explanation Video:

https://www.youtube.com/watch?v=b-0294YZjvk

Lily has only red and blue balls in a jar. If she removes three balls

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