• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

IAI November 2010 Examination Q3

P

paryas.bhatia

Member
Can we use combinations for solving this problem? If yes, please mention the solution.
 
Can we use combinations for solving this problem? If yes, please mention the solution.
(a)
Since p = 1/365 and q = 364/365
The probability of occurring one person's birthday is [1/365]
The probability of occurring two person's birthday is [1/365] * [1/365]
In a complete year
the probability of occurring two person's birthday is
[ [1/365] *
[1/365] * 365 ] = 0.002740

(b)
Say X is the number of birthdays, and hence X ~ Bin (3 , 1/365)
In a complete year occurring of at least two person birthdays is
P[ X => 2] * 365 = [ P [ X = 2 ] +
P [ X = 3] ] * 365
= [3C2 * (1/365)^2 * (364/365)^(3 - 2) + 3C3
* (1/365)^3 * (364/365)^0 ]
= 0.008204

Similarly

Say X is the number of birthdays, and hence X ~ Bin (4 , 1/365)
In a complete year occurring of at least two person birthdays is
P[ X => 2] * 365 = [ P [ X = 2 ] +
P [ X = 3] + P [ X = 4] ] * 365
= [4C2 * (1/365)^2 * (364/365)^(4 - 2) + 4C3
* (1/365)^3 * (364/365)^1 + 4C4 * (1/365)^4 * (364/365)^0 ] * 365
= 0.016356

(c)
Say X is the number of birthdays, and hence X ~ Bin (15 , 1/365)
In a complete year occurring of at least two person birthdays is
P[ X => 2] * 365 = [ 1 - P[ X < 2] ] * 365 = 0.25
 
Back
Top