Question 1042724: How strange are coincidences? Suppose an event has a 1 in 500 chance of happening each day. Won't you be surprised if it occurs? But approximately what is the probability that this event will happen sometime in the next year? (Hint: Assume independence, and find the probability that it will not occur in the next year. Round your answer to two decimal places.)
Found 2 solutions by ikleyn, robertb:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
How strange are coincidences? Suppose an event has a 1 in 500 chance of happening each day.
Won't you be surprised if it occurs? - Yes, I will.
But approximately what is the probability that this event will happen sometime in the next year?  .
(Hint: Assume independence, and find the probability that it will not occur in the next year. - I need not this hint.
Round your answer to two decimal places.)
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A catastrophe always happens suddenly. And unexpectedly. (the law I deduced myself).
Otherwise it is not a catastrophe.
Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website! I will interpret your problem this way: That the event has happened to you at a particular date this year, and then happens again to you exactly on the same date next year. By then, approximately 365 days have passed since the occurrence of the same event. At any day, the probability of the event happening is 1/500, hence the probability of it not happening at any day is 499/500. The re-occurrence of the event a year hence then follows the geometric distribution. The probability is given by
 ,
to three significant figures.
Meaning, there is 0.0965% chance of the same event happening a year hence. This, indeed, is surprising, and a strange coincidence, if it happens.
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