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10252013 #11
 Join Date
 Mar 2009
 Posts
 1
first reply for me, here. Linux and math fan, so:
about the 'birthday' question of the Cambridge test, here is my modest explanation:
If we have 3 guests, the probability that a fourth one has another birthday than the 3 others is P:
prob that she is not born the same day than the first: 364/365
and that she is not born the same day than the second: 363/365
and that she is not born the same day than the third: 362/365
simultaneously, so: P =364/365 * 363/365 * 362/365
The probability this fourth one has the same birthday as one
of the 3 others is, complementary: 1P
If we have n guests, P =364/365 * 363/365* ... * (366n)/365
Now we have to find n as 1P >= 1/2 or P <= 1/2
5 lines of Python code give n =23 (1P =0.507..)
Enjoy

10302013 #12
I have an issue with the question about the die. The question says that the die has the numbers to 6 on each side. I take that to mean that each side has the numbers 1 to 6. Therefore you will get the number six on every throw of the die. I'm sure that's not what they meant but if you ask a stupid question you get a stupid answer. The language used in one or two of the other questions was imprecise.

10312013 #13
 Join Date
 Mar 2009
 Posts
 1

10312013 #14
Depends on the wording of the question. If one person rolls the dice infinite amount of times, the average number of rolls between 6's will be 6. If you take infinite number of people and have them roll until they get a 6, the average number of rolls wil be 3.5, 1/6th of the people getting a 6 in 1 roll, 1/6th in 2 rolls etc. Only 1/6th of the people would require 6 rolls to get a 6.
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