Notes: What is the probability that 4 randomly selected people all have different birthdays? Round the answer to four decimal places

Tuesday, 15 September 2015

What is the probability that 4 randomly selected people all have different birthdays? Round the answer to four decimal places

There are 365
out of 365 ways to select the birthday of first person. Therefore the number of ways that we can
choose a birthday for second person is 364 out of 365.

Therefore the
probability of two persons not having the same birthday is,

$\displaystyle{P}{\left({2}\right)}=\frac{{365}}{{365}}$
xx364/365

For four people,

$\displaystyle{P}{\left({4}\right)}=\frac{{365}}{{365}}\times\frac{{364}}{{365}}\times$
363/365 xx 362/365

$\displaystyle{P}{\left({4}\right)}={0.9836}$

Therefore the probability of 4 people having different birthdays is
0.9836

Notes

Tuesday, 15 September 2015

What is the probability that 4 randomly selected people all have different birthdays? Round the answer to four decimal places

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