The Martian year is equal to 669 Martian days. Find the probability that there a
ID: 3181942 • Letter: T
Question
The Martian year is equal to 669 Martian days. Find the probability that there are (at least) two Martians with the same birthday in a group of (a) 2 Martians _____ (b) 3 Martians _____ (c) 15 Martians _____ Find the minimal size of a group such that the probability p that there are (at least) two Martians with the same birthday in such a group is greater than 0.5: _____ You come to a cafe to grab a coffee at a random time between 5 pm and 6 pm and spend 20 minutes in there. Independently, your friend comes to the same cafe at a random time between 5 pm and 6 pm and spends 20 minutes in there. Find the probability that you meet each other _____.Explanation / Answer
(5)
(a) Probability that 2 martians in a group of 2 have the same birthday is 1/669.
This is because first person can have the birthday on any of the day from 669 days and second person should have the same birthday. Hence 1/669*1 = 1/669
(b) In a group of 3, probability of at least 2 will have the same birthday is
3C2*(1/669) + 3C3*(1/669) = 4/669
(c) In a group of 15, lets find the probability that no two has same birthday. This probability is given by 1/669*1/668* . . . * 1/655
Hence required probability that at least two has same birthday is 1 - (1/669*1/668* . . . * 1/655)
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