1. If there are two basket ball players A and B. Player A scores with a probability of 0.7, B scores with probability 0.3. Both the players can take either 1 shot or 3 shots at the basket. Who should take which option and why?
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Probability roll 44 before 45
There are 100 prisoners on an island. Starring from Day 1, a guard will play the following game with them. On the n th day, a random prisoner will be brought into a room, which contains a switch that is either on or off. After he left the room, the guard will then ask the prisoner if everybody has been to the room. He can answer either "Yes" or "I dun know". If he answered "yes" and he is correct, everyone is free' otherwise everyone dies. If he answered "I dun know", the game continues: a prisoner will be choosen at random on (n+1)-th day and so on. Now these 100 prisoners are free to meet and discuss a strategy on the night of 0th day. Afterwards they will not be able to see anyone else at all. No other communcation is possible except the binary switch in the room. Is there a sure-fire strategy to free all of them?
1. There are 4 by 4 square grid pathways connecting southwest end and northeast end. How many different ways do exist? 2. Sum every numbers divisible by 7 under 1,000
99 lions and 1 sheep on an island, lions want to eat sheep but also want to stay alive, when a lion eats a sheep, it turns into a sheep. How many lions and sheep left after a period of time? (Lions can survive on other foods on the island, sheep cannot escape lions, all creatures are rational)
Q: For what integers b (other than zero) is it possible to find an integer a such that the ratio a/b is contained in the interval [.48, .52]?
What is 29^2?
A stick randomly breaks into 3 pieces, what is the possibility that it forms a triangle
A robot encounters a bunch of coins spread out on the ground. It examines each coin and, if the coin is heads, turns it to tails with 100% probability. If the coin is tails, it turns it to heads with 50% probability. He examines each coin once per cycle. If you have the robot cycle through the coins a very large number of times, what will eventually happen to the proportion of heads and the proportion of tails?
4. A spread set is a set where any two numbers in the set satisfies |x_i-x_j| > 2, how many spread set are there in {1,2,3,...,12}?
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