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  3. A jar contains only red, yellow, and orange marbles. If there are 3 red, 5 yello

A jar contains only red, yellow, and orange marbles. If there are 3 red, 5 yello

游客2024-01-14  49
问题 A jar contains only red, yellow, and orange marbles. If there are 3 red, 5 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
选项 A、 
B、 
C、 
D、 
E、 
答案 D
解析 It doesn’t really matter in which order we draw the marbles since they’re really all drawn at once, but from a mathematical standpoint, it’s much easier to take these probabilities one at a time. Let’s first take the probability of drawing a yellow marble from the jar. Since there are 5 yellow marbles out of 12 marbles total, the probability of drawing a yellow marble is 5/12 The probability of drawing a yellow marble after that is 4/11, since one yellow marble is missing and one marble is missing from the total. Finally, the probability of drawing a red marble is 3/10, So the probability of drawing the specified combination of marbles is . Once we reduce, we get 1/22 But since the order we draw in does not matter, we need to multiply this by the number of ways to arrange the three drawn marbles. It could be YYR, RYY, or YRY, for a total of 3 possible arrangements. So our total probability is  
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