1. An urn contains eight red balls, eight white balls, and eight blue balls, and sample of four balls is drawn at random without replacement.
Compute the probability that all of the balls in the sample are the same color. (Round your answer to four decimal places.)
2. In a suitable font, the letters A, H, I, M, 0, T, U, V, W, X, Y are all mirror images of themselves. A string made from these letters will be a mirror image of itself if it reads the same backward as forward: for example, MOM, YUMMUV, MOTHTOM. If a four-letter string in these letters is chosen at random, what is the probability that this string is a mirror image of itself? (Round your answer to four decimal places.)
3. An urn contains three red balls, five white balls, and two black balls. Three balls are drawn from the urn at random without replacement. For each red ball drawn, you win 58, and for each black ball drawn, you lose $12. Let X represent your net winnings.
Compute E(X), your expected net winnings. E(X) =
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