# Aptitude - Probability - Discussion

Discussion Forum : Probability - General Questions (Q.No. 12)
12.
A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
 1 22
 3 22
 2 91
 2 77
Explanation:

Let S be the sample space.

Then, n(S) = number of ways of drawing 3 balls out of 15
= 15C3
 = (15 x 14 x 13) (3 x 2 x 1)
= 455.

Let E = event of getting all the 3 red balls. n(E) = 5C3 = 5C2 = (5 x 4) = 10. (2 x 1) P(E) = n(E) = 10 = 2 . n(S) 455 91

Discussion:
32 comments Page 1 of 4.

Smrutiranjan Routray said:   3 months ago
Only red ball means;

5/15 * 4/14 * 3/13 = 60/2730 = 2/91.

Adnan Baig said:   4 months ago
Here it should be 5c3 becuase the selection of balls is 3 red balls.

SUDARSAN SWAIN said:   4 months ago
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Jino said:   2 years ago
@Deki Zangmo.

Thanks for the clear and best explanation.

Poojitha said:   2 years ago
Total balls are 15.

Only we have to select red balls in total balls red are 5.
One selected from a total 5/13.

Next, another selected (we have already selected one so 1 ball is reduced from both red balls and total balls) == 4/14.

Here, 2 balls are reduced 1 from one selected ball another from again selected ball so 3/13
5/15 * 4/14* 3/13 = 2/91.

Deki Zangmo said:   3 years ago
Total ball = 15.
Out of these, you have to select three balls.
15C3= 455,. We can select 3 balls in 455 ways.
But there is a condition that all 3 balls should be red so,
Out of 5 red balls we have to take out 3;
5C3 = 10,
As a result:
10/455 = 2/91.

Laxman said:   3 years ago
@USHA.

For example, there are 3 red balls and you have to select two balls out of it then possible ways are,
6 ways let me show;
R1,R2 R1,R3 R2,R1 R2,R3 R3,R1 R3,R1.

In these selections, we have R1, R2 and R2, R1 same like the way we consider only one so that we have 3 choices but don't consider you are selecting 3 out of 3 balls.

Pavanmahesh said:   3 years ago
All of them red balls means why it can be a 15c3?

Subash said:   4 years ago
Can any one explain clearly.

Sinchana said:   4 years ago
If the answer is 0.02 something how we can convert please explain it now.
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