A box contains 18 balls. 6 are black and 12 are white. A sample of 4 balls are taken with replacement, what is the probability that the sample contains no more than 2 black balls
I would really appreciate the help, thank you!
2026-04-11 23:54:25.1775951665
Probability that the sample contains no more than 2 black balls
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The probability that the sample contains no more than $2$ black balls is the probability that it contains $0, 1, $or $2$ black balls.
The probability that the sample contains no black balls is $$\left(\frac{12}{18}\right)^{4}$$ The probability that the sample contains one black ball is $$4\cdot \frac{6}{18}\cdot \left(\frac{12}{18}\right)^{3}$$ since there are $4$ orderings of the sample, and we need to draw one black ball and three white ones. Using this logic, can you find the probability that the sample contains two black balls? Once you have that, you are done.