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Two people have birthdays on different dates of the same 30

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Two people have birthdays on different dates of the same 30 [#permalink] New post 21 Feb 2012, 01:05
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Two people have birthdays on different dates of the same 30-day month. Assuming the dates of the birthdays are independent of one another, what is the probability the birthdays fall on the same day of the week each year?
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Re: Probability [#permalink] New post 21 Feb 2012, 05:41
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Smita04 wrote:
Two people have birthdays on different dates of the same 30-day month. Assuming the dates of the birthdays are independent of one another, what is the probability the birthdays fall on the same day of the week each year?


Smita04 wrote:
Two people have birthdays on different dates of the same 30-day month. Assuming the dates of the birthdays are independent of one another, what is the probability the birthdays fall on the same day of the week each year?


Think of what the calendar of a 30-day month would look like:

Mo Tu We Th Fr Sa Su
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30

In how many ways can we ensure that both the dates fall on the same day of the week?
From the first column, we could select any two dates in 5C2 ways. Say, we get 01 and 15. Every year, whatever is the day on 1st of June, it will be the same day on 15th of June.
Same for the second column so we have another 5C2 ways.
For the rest of the 5 columns, we select two dates out of 4 in 4C2 ways.
Total ways in which both dates fall on the same day each year = 2*(5C2) + 5*(4C2) = 20 + 30 = 50
There are a total of 4 30-day months so total ways = 4*50

Total number of ways of selecting 2 dates from a 30 day month = 30C2 = 435
Again, since there are 4 30-day months, total number of ways = 4*435

Required Probability = 4*50/4*435 = 10/87
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Re: Probability   [#permalink] 21 Feb 2012, 05:41
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