Question

Four kinds of apples are mixed in a box. How many apples must you take to be sure of at least 5 apples of one kind?​

Answer 1

Answer:The answer is 4, since in the most unfavorable case you take out one apple of each kind and successively another apple of one of the three kinds.

1. Explanation:If there are only 3 kinds of Apple then we need to take out 4 apples so that there are atleast two apples of one kind .For any k kinds of apple , we need k+1 selections.
2. This depends on how many of each kind. If you only had 1 of each, then it is impossible.
4. If you have at least 2 of at least one type though, then the answer is 4. Let’s say that the three types of apples are A, B, C. On the first draw, you draw out an A. Then on the second draw, say you draw a B. Then on the third draw, you draw a C. On the fourth draw, no matter what other apples are in the barrel, you have to draw either an A, a B, or a C, making a matching pair.
6. To summarize, the answer is either “it is impossible” or 4
7. You must take at least one apple more than the number of varieties in the box. This is easy to chart:
9. 1: Only one type of apple possible.
11. 2: Odds of second apple being of the same type is 1:3. If not, get another.
13. 3: Since we only draw this apple if the first two are of different types, odds of third apple being the same as one of the previous two is 2:3.
15. 4: The fourth apple must match one of the previous types, since we now have one of each type (or we wouldn’t get this far). So the odds of the fourth apple being a duplicate is 3:3, or 100%. This is the only way to be certain that you have at least two apples of the same variety; any lesser number affords the possibility that you do not.
16. Suppose you take one apple of one variety at random
18. the other two of same variety.- one way.
20. On the other hand if you take one of two variety at random it is possible that second time you take the same variety.-two ways.
22. If second time you take one of one variety then you get
24. the other one of two variety in the third time.- three ways.