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Difficulty:
25%
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Question Stats:
72% (00:50) correct
28%
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wrong
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What is the probability that two siblings, ages 6 and 8, will have the same birthday, assuming neither was born in a leap year?
A. 1/133225
B. 1/365
C. 1/48
D. 1/14
E. 1/2
A. 1/133225
B. 1/365
C. 1/48
D. 1/14
E. 1/2
A. 1/133225 - I thought this was the correct answer, because from what I understand if we want to find out the prob that BOTH siblings will have the same birthday is much higher than just 1/365. Even though they are independent events, which is 1/365 per time a child is born, in order for both of your child to have the same bday the odds presumably increases. Can someone please correct my logic. Thanks.
22 Jan 2016, 09:38
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probability of one person born on 1st january is = 1/365
probability of other being born on 1st january is = 1/365
probability of first AND second born on 1st january is = (1/365)*(1/365)
now they can be born on 2nd jan OR 3rd jan OR 4th jan..... OR any day out of the 365 days of the year.
hence probability = (1/365)*(1/365) + (1/365)*(1/365) + (1/365)*(1/365) ........ add 365 times = 365*(1/365)*(1/365) = 1/365
probability of other being born on 1st january is = 1/365
probability of first AND second born on 1st january is = (1/365)*(1/365)
now they can be born on 2nd jan OR 3rd jan OR 4th jan..... OR any day out of the 365 days of the year.
hence probability = (1/365)*(1/365) + (1/365)*(1/365) + (1/365)*(1/365) ........ add 365 times = 365*(1/365)*(1/365) = 1/365
02 May 2012, 14:44
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The first sibling is born on a given day, that probably is 1/1. The probability of the second having a birthday on the same day is 1/365.
You have to think as the two as independent events. The probably of one person having a birthday on ANY date is 1/1, not 1/365. The second has to match.
You have to think as the two as independent events. The probably of one person having a birthday on ANY date is 1/1, not 1/365. The second has to match.
