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Discovering that your three best friends were all born on a Sunday?

Discovering that your three best friends were all born on a Sunday?

Math   Statistics-And-Probability   
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Answer #1

For a sample space of 400 years,

there are 97 leap years

So, probability of getting a leap year = 97/400= 0.2425

For a leap year(366 days),  

Probability of 53 Sunday's = 2/7

Probability of 52 Sunday's = 5/7

For non leap year(365 days),

probability of 53 Sunday's = 1/7

Probability of 52 Sunday's = 6/7

Required probability that three best friends were all born on Sunday's = 0.2425* ((5/7)*(52/366)3 +(2/7)*(53/366)3)+ 0.7575*((6/7)*(52/365)3+(1/7)*(53/365)3)

= 0.2425*0.002916 + 0.7575*0.0029158476

=0.247624754 = 0.247625

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