
Russ P. answered 12/30/14
Tutor
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Patient MIT Grad For Math and Science Tutoring
Habeeba,
If I understand your slightly garbled question, there can be many different probability scenarios that will map to your probability answer of 5/13. Hence, there is no one unique answer. For example:
Consider a standard deck of 52 playing cards. Probability 5/13 is same as 20/52 since I just multiplied top and bottom by 4. Shuffle the deck, pick one card and note its value, replace it in the deck and reshuffle. Do this 4 times. What then is the probability that all four cards you picked is in the range [2, 3, ...6]?
Since each time you picked a card the conditions were the same (full 52 card deck reshuffled), the probabilities are identical. Thus
Answer = (4 suits ) (5 cards in the range)/52 = 20/52 = 5/13.
You can come up with variations on this example to see that many scenarios can produce the same answer.