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Serggg [28]
2 years ago
10

Suppose that 3 balls will be randomly put into 3 buckets, with each ball being equally likely to be put into each of the buckets

, independently of which buckets are chosen for any of the other balls. (E.g., the first ball is equally likely to be put into any of the 3 buckets, and then regardless of which bucket the first ball is placed in, the second ball is equally likely to be put into any of the 3 buckets.) What is the probability that all of the balls will be put into the same bucket
Mathematics
1 answer:
Yuliya22 [10]2 years ago
8 0

Answer:

\frac{1}{27}

Step-by-step explanation:

Since there are a total of three buckets and only one can be chosen at a time, this would mean that the probability of a ball being placed in a bucket is 1/3. Since each ball has the same probability of being placed into any bucket regardless of the where the previous ball landed, it means that each ball has the same 1/3 probability of a bucket. In order to find the probability that all three land in the same bucket, we need to multiply this probability together for each one of the balls like so...

\frac{1}{3} * \frac{1}{3} * \frac{1}{3}  = \frac{1}{27}

Finally, we see that the probability of all three balls landing in the same bucket is \frac{1}{27}

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