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Sampling with replacement

ProbabilityEasy

An urn holds $4$ green and $6$ white balls. You draw a ball at random, note its color and put it back, and you repeat this $3$ times in total. What is the probability that exactly $1$ of the drawn balls is green?

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Hint

The draws are independent; count the positions where the green ball can appear.

Solution

Each draw is green with probability $0.4$ and white with probability $0.6$ , independently.
There are $3$ positions for the single green ball.
Each such sequence has probability $0.4 \times 0. 6^{2}$ .
So the probability is $3 \times 0.4 \times 0.36$ , which equals $0.432$ .

Answer: $0.432$

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