(a). In a group of 6 people, what is the probability that at least two of them h

Question

(a). In a group of 6 people, what is the probability that at least two of them have the same birthday (day and month)? For simplicity, forget about leap year. That is, assume 365 days in a year. Also assume all the days are equally likely to be someone's birthday. (b). Answer part (a) for a group of 20 people.    (c). How many people must be in the group for the probability of at least two having the same birthday to reach 50%? 90%? To answer this question, you will need to use a formula and either a spreadsheet/table or a graphing utility.

Explanation / Answer

a) probability that at least two of them have the same birthday =1-P( none of have same birthday)

=1-(365*364*363*362*361*360)/3656 =1-0.9595 =0.0405

b) for 20 peopole   probability that at least two of them have the same birthday =1-(365)!/((365-20)!*36520)

=1-0.5886 =0.4114

c) let for above to reach 50% ; let number of people required =n

therfore 0.5 >1-(365)!/((365-n)!*36520)

solving above n =23

similarly for  above to reach 50% ; let number of people required =n

0.6 >1-(365)!/((365-n)!*36520)

solving above n =27

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.