I can't seem to put the Fundamentals of Counting to good use... I have such a hard time answering probability questions with the rules of counting. Here's one question that blew my mind:(adsbygoogle = window.adsbygoogle || []).push({});

There are 4 persons. The sample space E consists of the events E={E1, E2, E3, E4, E5 }. Let E1 be the event that all four person have the same birthmonth, E2 be the event that exactly 3 of them have the same birthmonth, E3 be the event that exactly 2 of them have the same birthmonth while the remaining 2 have different birthmonths, E4 be the event that two have the same birthmonths and the other two have the same birthmonths, and E5 be the event that all four person have different birthmonths. Assign probability measures to each and find the probability that at least 2 persons have the same birthmonth. Note that the sample space is E1 U E2 U E3 U E4 U E5 (meaning that they are disjoint).

I know that you need to use Baye’s Theorem and the Rule of Elimination to find the probabilities of the difficult event… the only problem is I find it difficult to find the probabilities of events E1 to E5 ‘cause my knowledge of the fundamentals of counting suck (I hate to admit it). Can anyone help me out and give pointers on when to use the fundamentals of counting when given questions such as the one above?

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# Probability Question that involves alot of counting

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