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Determine the probability that at least 2 people in a room of 11 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions: (a) Compute the probability that 11 people have different birthdays. (b) The complement of "11 people have different birthdays" is "at least 2 share a birthday". Use this information to compute the probability that at least 2 people out of 11 share the same birthday.

          Determine the probability that at least 2 people in a room of 11
people share the same birthday, ignoring leap years and
assuming each birthday is equally likely, by answering the
following questions:
(a) Compute the probability that 11 people have different
birthdays.
(b) The complement of "11 people have different birthdays"
is "at least 2 share a birthday". Use this information
to compute the probability that at least 2 people out of 11 share
the same birthday.
        
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Added by Daniela P.

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Determine the probability that at least 2 people in a room of 11 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions: (a) Compute the probability that 11 people have different birthdays. (b) The complement of "11 people have different birthdays" is "at least 2 share a birthday". Use this information to compute the probability that at least 2 people out of 11 share the same birthday.
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Transcript

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00:01 So in this question, we want to work out the probability that two people in a room of 11 share the same birthday.
00:07 So first of all, what's the probability that all 11 people have different birthdays? so probability 11 different birthdays.
00:21 Let's call that p.
00:23 So p is going to be, so for the first person, they can be born on any day of the year, 365 over 365.
00:31 For the second person, they can't be born on the same day as the first person.
00:35 So there's a 364 over 365 chance.
00:40 For the third person, they can't be born on any of the same two days as the first ones.
00:45 So we've got 363 over 365.
00:48 And we're going to go all the way down to 365 minus 10 is 355 over 365.
01:00 So what's this? well, it's 365 factorial, divided by 365 to the power of 11, times...
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