Probability Puzzles

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write ‘pass’.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?View SolutionSubmit Solution 219.1K views
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A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by one the girls come and pick a dress.
What is the probability that no girl will choose her own dress?View SolutionSubmit Solution 355.8K views
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A man has 53 socks in his drawer: 21 identical blue, 15 identical black and 17 identical red. The lights are fused and he is completely in the dark.
How many socks must he take out to make 100 per cent certain he has a pair of black socks?
View SolutionSubmit Solution 639.2K views
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Three people are in a room. Ronni looks at Nile. Niile looks at Senthil. Ronni is married but Senthil is not married. At any point, is a married person looking at an unmarried person? Yes, No or Cannot be determined.
View SolutionSubmit Solution 673.9K views
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There are two Jars with 50 balls each black and white mix in colour. You have to pick a random ball from a random bowl. How do you maximise the probability of getting a black ball ?
Submit Solution 674.6K views
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You have a GPS that takes 2 working batteries. You have 8 batteries but only 4 of them work.
What is the fewest number of pairs you need to test to guarantee you can get the GPS on.View SolutionSubmit Solution 680.2K views
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Jacob & John have two children. The probability that the first child is a girl is 50%. The probability that the second child is a girl is also 50%. Jacob & John tell you that they have a daughter.
What is the probability that their other child is also a girl?
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A jar contains one hundred marbles, each of which may be white or black. You pull out 100 marbles with replacement, and they are all white. What is the probability that all one hundred marbles are white?
(Note: “With replacement” means you take out a random marble, look at its colour, then put that marble back. Then repeat.)
View SolutionSubmit Solution 869.0K views
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Jacob and John are competing for the same girl. After years of battling, both decide to settle it by tossing a coin.
John produces a coin, but Jacob doesn’t happen to have one on him. Jacob is sure that the coin John has produced is loaded, i.e. it will come up with heads more than 50% of the time on average.
How do Jacob arrange a fair contest, based purely on chance and not skill, by flipping this coin?
Variation: (COIN BIASING) Jacob and John are competing for the same girl, and decide to settle it with a coin toss. John has known the girl longer than Jacob have, so Jacob agree that it is fair for him to have a chance of winning equal to P, where P > 0.5. However, Jacob only have a fair coin. How can you conduct this contest such that the biased probability is manifested? What is the average number of coin flips needed to determine a winner?
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