Suppose there are exactly 365 days in a year and suppose that birthdays are unif

Question

Suppose there are exactly 365 days in a year and suppose that birthdays are uniformly distributed among these days. Given a group of n people, the probability that they will all have different birthdays is

(1) There is an amusing fact called the Birthday Paradox which says that given a group of n, people there is more than 50% chance that at least one pair in that group shares a birthday. This value of n is smaller than most people expect, hence the name. Use MATLAB to find the value of n.

(2) If there are 78 people in a room, What is the probability that everyone in that group has a different birthday?

n Probabilty Comments 1 365/365 I'm the only one! 2 (365/365)*(364/365) Since the new person must have a birthday in one of the other 364 days 2 (365/365)*(364/365)*(363/365) et cetera

Explanation / Answer

The formula is (365/365)*(364/365)*(363/365) and so on.

(1)

val = 1;

for j = 365:-1:1
val = val*((j*1.0)/365);
if(val<0.5)
break
end
end
disp(366-j);

The answer is 23.

(2)

The answer is 1.39*10^(-4)

val = 1;

klk = 365-78+1;

for j = 365:-1:klk
val = val*((j*1.0)/365);
end
disp(val);

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