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I have 3 buckets with billiards balls placed as below

  • Bucket 1: Balls 1 to 5
  • Bucket 2: Balls 6 to 10
  • Bucket 3: Balls 11 to 15

 

  1. What is the probability of picking 3 balls at random with one from each bucket?
  2. What is the probability of picking 3 balls at random with one from each bucket, with replacement?

Thanks in advance.

What I tried:

The probability of choosing 1st bucket is 1/3 probability of choosing 2nd bucket is 1/3 probability of choosing 3rd bucket is 1/3

Probability of picking up a ball from 1st bucket = 1/5.

Probability of picking up a ball from 2nd bucket = 1/5

Probability of picking up a ball from 3rd bucket = 1/5

So,

Probability of choosing one from 1st bucket

( probability of choosing 1st bucket) x (probability of choosing one ball from 1st bucket) .

(1/3)* (1/5)= 1/15.

similarly from 2nd bucket

(1/3) * (1/5) = 1/15

similarly from 3rd bucket

(1/3)*(1/5) = 1/15

The final probability of picking 3 balls from 3 buckets

1/15 + 1/15 + 1/15 = 3/15

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    $\begingroup$ What have you tried? Note: I'm not sure the problem is clear. How are you selecting the balls? Is it "without replacement" for part $1$? $\endgroup$ – lulu Feb 4 at 22:17
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    $\begingroup$ HINT for 1) divide the number of ways to pick one from each bucket by the number of ways to pick 3 from all 15 $\endgroup$ – Bram28 Feb 4 at 22:19
  • $\begingroup$ I pick 3 balls at random no selection. And yes the first one is without replacement $\endgroup$ – Rob Feb 4 at 22:19
  • $\begingroup$ Welcome to MathSE. When you pose a question here, it is expected that you include your own thoughts on the problem. Please edit your question to show what you have attempted and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site. $\endgroup$ – N. F. Taussig Feb 4 at 22:27
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    $\begingroup$ To amplify on the previous comment: if we put all 15 balls in one bucket, I could shake the bucket vigorously, reach in without looking and stir the balls around, then (still without looking) grasp whichever ball I can and draw it from the bucket. It is reasonable to suppose the each ball has an equal chance of being chosen, and if I reach in a second and third time, each ball in the bucket at that time has an equal chance to be chosen. But if I have three buckets, what's the procedure? I can only reach into one bucket at a time. $\endgroup$ – David K Feb 5 at 4:58

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