PRACTICE ANOTHER
Let $X_1, X_2, X_3, X_4, X_5$, and $X_6$ denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size $n$. Then these $X$'s have a multinomial distribution. Suppose
it is claimed that the color proportions are $p_1 = 0.25$, $p_2 = 0.13$, $p_3 = 0.15$, $p_4 = 0.2$, $p_5 = 0.12$, and $p_6 = 0.15$.
USE SALT
(a) If $n = 12$, what is the probability that there are exactly two M&Ms of each color? (Round your answer to four decimal places.)
(b) For $n = 20$, what is the probability that there at most eight orange candies? [Hint: Think of an orange candy as a success and any other color as a failure.] (Round your answer to three decimal
places.)
You may need to use the appropriate table
