Question

Find the chance that the 5 people have 5 different birthdays.

Here is my workings but I think I have gone wrong somewhere

364/365*364/365*363/365*362/365*361/365= I can't seem to get it right have I calculated something wrong?

Answer 1

= 1 - probability that 2 people have the same birthday

Answer 2

sorry, rephrase:
= 1-[(probability that any 2 people have the same birthday)+(probability that any 3 people have the same birthday)+(probability that any 4 people have the same birthday)+(probability that any 5 people have the same birthday)

Answer 3

it is a bit like that but I am looking at five people with five different birthdays. I just want to know I am on the right track.

Answer 4

not great with probability sorry, will get:
@Mertsj @amistre64 @hartnn @Callisto @mathslover
these guys are the beez neez

Answer 5

maybe they're not on right now, will try:
@UnkleRhaukus and @hba pretty please?

Answer 6

was thinking now that the answer is
1-probability that 5 people have the same birthday...?

Answer 7

ok think I have worked it i.e. -1 1 person 365 2 364 3 363 4 362 and 5 361 do we mutiple all these with 365 days excluding a leap year? that is five people with five diffrent birthdays

Answer 8

ideas @hba ??

Answer 9

my idea is, and it could be faulty ......

\[\binom{5}{5}\left(\frac{1}{365}\right)^{5}\left(\frac{364}{365}\right)^{0}\]

Answer 10

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i think the count for 5 people is 1+5+10+10+5+1 = 32 different scenarios

Answer 11

the probability that any given person has a birthday on a given day is 1/365, so the compliment of that is 364/365

Answer 12

...lol, never did like this particular one. satelitte has it tattoed someplace im sure

Answer 13

finding the chance that they have the same birthday might be easier; then its just 1-same birthdays