SOLUTION: A box contains 24 pieces of fruit: 7 cherry, 8 orange and 9 lemon. If no cherries are sold, what is the minimum number of lemons that can be sold in order to increase the probabili

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Question 1141623: A box contains 24 pieces of fruit: 7 cherry, 8 orange and 9 lemon. If no cherries are sold, what is the minimum number of lemons that can be sold in order to increase the probability of picking out a cherry to 50%?
A)0
B)1
C)2
D)3
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Unfortunately none of these choices work. Let's go through them one by one to see why.
  1. If you sold 0 lemons, then the chances of picking a cherry are 7/24 = 0.2917 = 29.17% approximately
  2. If you sold 1 lemon, then the chances of picking a cherry are 7/23 = 0.3043 = 30.43% approximately
  3. If you sold 2 lemons, then the chances of picking a cherry are 7/22 = 0.3182 = 31.82% approximately
  4. If you sold 3 lemons, then the chances of picking a cherry are 7/21 = 1/3 = 0.3333 = 33.33% approximately
As you can see, we don't get anywhere close to 50%. The highest we get is roughly 33.33%

So there seems to be a typo with this problem. Please ask your teacher for clarification and/or corrections.

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Side note: If we sold all 9 lemons, then the only way to have a 50% shot at getting a cherry is that we must have the same number of cherries and oranges. The fact that we have 7 cherries and 8 oranges means that the chances of picking a cherry are less than 50%. This is because there are less cherries compared to oranges.
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