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How was this answer derived?
I once read a riddle in a magazine that deals with probability. The answer was given in a different issue, but I never found out why that was the answer. Could someone help me there?
The minister for transport wants as many students to get week passes as weekend passes for public transport. He takes a large pile of envelopes and puts week passes in half of them, and weekend passes in the other. When they are on the belt to send them off, the Prime Minister sees the envelope for his son pass by and quickly adds a weekend pass. After a bit, a councillor spots an envelope with two passes. He takes one out: a weekend pass.
What is the probability that the son of the Prime Minister is stuck with a weekend pass?
The answer was given as 2/3. I have no clue how this was obtained. Can someone enlighten me?
I'm looking for a mathematical basis for this answer. I can get to the point where it was 50% because of the starting question, but how does adding a weekend pass change the odds?
2 Answers
- 1 decade agoFavourite answer
Based on how this question is written...
The prime ministers son originally has one of two possible passes: weekend or weekday, with equal probability.
But then the prime minister puts a weekend pass into his sons envelop. Thus, the son either has one of two possible envelops: a weekend AND a weekday, or two weekends.
Then the counselor takes a weekend out. We are totally ignorant of which of the above two situations we are in, thus there are three different weekend passes involved, and any one of them is taken out with equal probability.
We are left with: weekday in the first envelope and in the second envelop either the original weekend or the added weekend.
There are three possibilities: Weekday, original weekend, or added weekend.
Thus there is a 2/3 chance of it being a weekend pass.
- 1 decade ago
because the son has 3 choices of what he has... a week pass, a weekend pass or both, if the son has both he has a weekend and if he only has weekend a weekend but if he has week he dunt so its 2/3
