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An urn contains 8 white and 5 red balls. Four balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 4 balls drawn from the urn are white? Round your answer to three decimal places.



Answer :

Let's first compute the probability of one (or the first) trial, when the drawn is white.

Total balls = 13

White balls = 8

[tex]P(\text{whites)}=\frac{8}{13}[/tex]

Now, everytime a replacement happens we will have the same amount of balls for the next trial. Therefore, the probability of whites will be multiplied for each trial:

[tex]P(\text{whites)}=(\frac{8}{13})^4=0.143[/tex]

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