Statistics Probability

Statistics
Tutor: None Selected Time limit: 1 Day

If you ask for strangers about their birthdays, what is the probablility: all were born on Wednesdays? None were born on Saturday? All were born on different days of the week?

Can you explain what type of probability problem this is called and how to figure it out. 

Thanks!

Jul 21st, 2015

Thank you for the opportunity to help you with your question!

Let us assume that you asked with n number of strangers about their birthdays, then the probability of all were born on Wednesday can be found as follows

P(all strangers were born on Wednesday) = (1/7)^n 
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Probability that none were born on a Saturday can be calculated as follows

P(none of them born on Saturday) =(6/7)^n

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P(all born on same day) = 7(1/7)^n

P(2 born on same day) = 7(1/7)^2(6/7)^(n-1)   & so on ....
--
Therefore

P(all on different day) = 1 - [P(all on same day) + P(2 on same day)+ P(3 on same day) + ---- P(n-1) on same day]

to understand this problem more clear number of strangers must be given in problem !!

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Jul 21st, 2015

I apoligize I was typing it out fast... I put "for" instead of "4"

Jul 21st, 2015

My question is now, I get a very weird number when I plug in 1/7^4 ...Would I express my answer as 1/7^4 and leave it as that?

Jul 21st, 2015

oh...

1. P(all strangers were born on Wednesday) = (1/7)^4 =   1/2401

2. P(none of them born on Saturday) =(6/7)^n = (6/7)^4 = 1296/2401

3.P(all on different day) = 1 - [ (1/7)^4 +(1/7)^3 (6/7)^1 + (1/7)^2 (6/7)^2]  

= 1-  [ 1/2401 + 6/2401  + 36/2401] = 1-43/2401 =2358/2401

Jul 21st, 2015

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