Mathematics, 17.07.2020 05:01, vetterk1400
(a) (i) Find the probability of getting at least one 3 when 9 fair dice are thrown. (ii) When n fair dice are thrown, the probability of getting at least one 3 is greater than 0.9. Find the smallest possible value of n. (b) A bag contains 5 green balls and 3 yellow balls. Ronnie and Julie play a game in which they take turns to draw a ball from the bag at random without replacement. The winner of the game is the first person to draw a yellow ball. Julie draws the first ball. Find the probability that Ronnie wins the game.
Answers: 3
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![=1-[{9\choose 0}(\frac{1}{6})^{0}(1-\frac{1}{6})^{9-0}]\\\\=1-(\frac{5}{6})^{9}\\\\=1-0.19381\\\\=0.80619\\\\\approx 0.8062](/tpl/images/0708/3368/baa9a.png)
![=[\frac{5}{8}\times \frac{3}{7}]+[\frac{5}{8}\times \frac{3}{7}\times \frac{4}{6}\times \frac{2}{5}]+[\frac{5}{8}\times \frac{3}{7}\times \frac{4}{6}\times \frac{2}{5}\times \frac{1}{4}\times 1]\\\\=0.2679+0.0714+0.0179\\\\=0.3572](/tpl/images/0708/3368/e01ca.png)
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(a) (i) Find the probability of getting at least one 3 when 9 fair dice are thrown. (ii) When n fair...
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