You have a jar with 60 jelly beans. you know that 1/3 of the jelly beans are yellow, 1/4 of them are white and the rest is red. You are not allowed to look. How many beans do you have to take out to be absolutely sure to get at least one yellow one?

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Deangelo Hurst

Mathematics

29 September, 02:51

You have a jar with 60 jelly beans. you know that 1/3 of the jelly beans are yellow, 1/4 of them are white and the rest is red. You are not allowed to look. How many beans do you have to take out to be absolutely sure to get at least one yellow one?

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Eli Grant · Answer 1

First, we evaluate the number of jelly beans of each color. Yellow are: 1/3 x 60 = 20. White are 1/4 x 60 = 15. Red are: 60 - 15 - 20 = 25. Now, as slim as the chance is, it is possible that you draw no yellow beans until all of the remaining beans have been depleted. Therefore, the maximum number of beans you must remove from the jar to get at least one yellow is one plus the sum of non-yellow beans. Total non-yellow beans are 25 + 15 = 40 non-yellow beans. Therefore, you must remove 41 beans from the bag to be absolutely sure to get a yellow, because in every draw before the 41st draw, there is a chance to get a bean that is not yellow.