Geeta and Seeta are friends. What is probability that both will have -

i) different birthday

ii) the same birthday (ignoring a leap year)

Let A denote the event that Geeta and Seeta have the same birthday.

and

 https://s3mn.mnimgs.com/img/shared/discuss_editlive/mathmlequation352155306925886246.png denote the event that Geeta and Seeta have different birthday.

 

If Geeta and Seeta  have the same birthday,

then their birthday could be on any one of the days from 365 days of the year.

 

 Number of cases in favourable of event A = 1

 

Required probability, P(A) = https://s3mn.mnimgs.com/img/shared/editlive_temp/mathmlequation239104344719086947.png

 

As, we know that,

 P(A) + P( https://s3mn.mnimgs.com/img/shared/discuss_editlive/mathmlequation34012414612355232.png) = 1

 

https://s3mn.mnimgs.com/img/shared/discuss_editlive/mathmlequation5884742599872146223.png

Probability that Geeta and Seeta have the same birthday = https://s3mn.mnimgs.com/img/shared/discuss_editlive/mathmlequation8280412799490598593_3194969004800280714.png

Probability that Geeta and Seeta have different birthday = https://s3mn.mnimgs.com/img/shared/discuss_editlive/mathmlequation4314919844115516632_1445688268492700190.png

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i Total no. of possible outcomes = 365

They cannot have the same birthday on 364 days 

So, probability = 364/365

ii Total possible outcomes = 365

No. of days they can have same birthday = 1

So probability = 1/365

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