This exercise is on probabilities and coincidence of shar ed birthdays. Complete

Question

This exercise is on probabilities and coincidence of shar ed birthdays. Complete parts (a) through (e) below a lf two people are selected at random. the probablity that they do not have the same birthday (day and mont) is 65 364 e·i Expla The first person can have any birthday, so they can have a bithday on 365 of the 365 days In order for the second person to not have the same birthday they must have one of the 364 remaining birthd (Type whole numbers) b If four people are selected at random, find the probability that they all have different birthdays The probability that they all have different birthdays is 0.984 (Round to three decimal places as needed ) c If four people are selected at random, find the probability that at least two of them have the same birthday The probability that at least two of them have the same bithday is Round to three decimal places as needed)

Explanation / Answer

(a)

If there are 2 people, the chance that they do not have the same birthday is 364/365
so the chance that they do have the same birthday is
   1-(364/365)
if there are 3 people you and 2 others the chance that neigther of the other two sahres your specific birthday is
(364/365)*(364/365)
however the other two might have the same birthday .the chance that all 3 people have different birthday is
P(None of the three shares the same birthday)=(354/365)(363/365)
                                                                  =0.992

(b)

The first person will *not* match anyone's birthday because he/she is the first in the room.
P(first person has unique birthday) = 365/365 = 1

The second person will *not* match the first person's birthday 364 out of 365 times.
P(second person has unique birthday) = 364/365

The third person will *not* match the other two person's birthdays 363 out of 365 times.
P(third person has unique birthday) = 363/365

The third person will *not* match the other two person's birthdays 363 out of 365 times.
P(third person has unique birthday) = 362/365

Multiply to find the combined probability:
P(none match) = 1* 364/365 * 363/365*362/365
                        =0.9972*0.9945*0.9917
                         =0.9834

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