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A bag contains 26 purple jellybeans, 15 green jellybeans, and 9 yellow jellybeans; these jellybeans are the only items in the bag. If a person reaches into the bag and picks out only purple jellybeans, how many jellybeans would the person have to pick out in order to double the probability that a jellybean picked out of the bag at random would be a green jellybean? A. 5 B. 15 C. 19 D. 24 E. 25

A bag contains 26 purple jellybeans, 15 green jellybeans, and 9 yellow jellybeans; these jellybeans are the only items in the bag. If a person reaches into the bag and picks out only purple jellybeans, how many jellybeans would the person have to pick out in order to double the probability that a jellybean picked out of the bag at random would be a green jellybean? A. 5 B. 15 C. 19 D. 24 E. 25

The total number of jellybeans in the bag was intially 50. And the probability of picking out the green jellybeans was 15/50. But after choosing one purple jellybean the total number of jellybeans in the bag is 49. Hence, the probability of picking out the green jellybeans thereafter is 15/49. In order to double the probability that a jellybean picked out of the bag at random would be a green jellybean the person should pick 24 more out of 49 jellybeans. Henceforth, the probability of picking out the green jellybeans will be doubled, i.e. 15/25 or 3/5 because the initial pprobability was 15/50 or 3/10.

To solve this problem, you would first need to figure out what it means to double the probability of picking a green jellybean at random. Your first step would be to determine the initial odds of picking a green jellybean; we know from the last question that those odds are 15/50 = 0.3 = 30%. Doubled odds, therefore, are 60%, or 0.6. Since the person picking out the jellybeans in this question is picking only purple jellybeans, we know that the number of green jellybeans remains the same, 15. If x is the new total of jellybeans after the person picks out the purples, we can set up the equation:

0.6=15/x => x=25

So the new total of jellybeans must be 25. If the original total was 50, a person would have to pick out 50 – 25 = 25 purple jellybeans in order to double the probability of picking a green jellybean at random.

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