Question 1112835: A bag contains 7purple and 6 red jelly beans. What is the probability that 2 red jelly beans will be pulled?
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443)   (Show Source):
Answer by solver91311(24713)  (Show Source):
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Depends. If you draw a red one on the first draw, do you replace it before you draw the second one or not?
There are a total of 13 jelly beans in the bag, 6 of which are red. So the probability of drawing a red one on the first draw is  .
If a purple bean is drawn on the first draw, then the experiment has failed and it doesn't matter what happens on the second draw regardless of replacement.
If a red bean is drawn on the first draw and IS replaced, then the probability that a red bean will be drawn on the second draw is the same as that for the first draw, and the overall probability is the product of the two individual probabilities, to wit \(\frac{6}{13}\)\ =\ \frac{36}{169})
If a red bean is drawn on the first draw and IS NOT replaced, then the probability of drawing a red bean on the second draw has changed. Since the bag is now missing one red bean, there are still seven purple beans, but only five red beans and the total number of beans has been reduced by one from 13 to 12. Hence, the probability of drawing a red bean on the second draw is  . Since adjusting for the changed composition of the contents of the bag accounts for the fact that the overall experiment is not two independent events when the experiment is conducted WITHOUT replacement, the overall probability is still the product of the two individual probabilities: \(\frac{5}{12}\)\ =\ \frac{15}{78})
John
My calculator said it, I believe it, that settles it
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