Q41: You’re about to get on a plane to Seattle. You want to know if it’s raining. You call 3 random friends who live there and ask each if it’s raining. Each friend has a 2/3 chance of telling you the truth and a 1/3 chance of messing with you by lying. All 3 friends tell you that “Yes” it is raining. What is the probability that it’s actually raining in Seattle?
Q42: A Russian gangster kidnaps you. He puts two bullets in consecutive order in an empty six-round revolver, spins it, points it at your head and shoots. *click* You’re still alive. He then asks you, “do you want me to spin it again and fire or pull the trigger again right away?” For each option, what is the probability that you’ll be shot?
Q42: A Russian gangster kidnaps you. He puts two bullets in consecutive order in an empty six-round revolver, spins it, points it at your head and shoots. *click* You’re still alive. He then asks you, “do you want me to spin it again and fire or pull the trigger again right away?” For each option, what is the probability that you’ll be shot?
Q43: There are 20 different socks of two types in a drawer in a completely dark room. What is the minimum number of socks you should grab to ensure you have a matching pair?
Q44 How many trailing zeros are in the number 5! (5 factorial)?
Q45: You have a 100 coins laying flat on a table, each with a head side and a tail side. 10 of them are heads up, 90 are tails up. You can’t feel, see or in any other way find out which 10 are heads up. Your goal: split the coins into two piles so there are the same number of heads-up coins in each pile.
Q46: If you have a square room with no roof, and you had four flagpoles you had to plant on the walls so that each flagpole touched two walls, how would you do it?
Q47: There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of its box. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?
Q48: You have a 100 coins laying flat on a table, each with a head side and a tail side. 10 of them are heads up, 90 are tails up. You can’t feel, see or in any other way find out which 10 are heads up. Your goal: split the coins into two piles so there are the same number of heads-up coins in each pile.
Q49: There are 27 coins and a two-pan balance. All coins has same weight except for one, which is heavier than all others. All coins looks identical. What is the minimum number of weighing required to certainly find out heavier coin?
Q50: Two persons are walking into a railway tunnel. Upon crossing 2/3rd of the tunnel, they saw a train is coming from opposite direction. Each person ran for a different end of tunnel with speed of 10 km per hour. Fortunately, both persons escaped from the tunnel just right time i.e.. at the time train would have run through them. Assuming train was running with a constant speed and both persons reacted immediately, Find out speed of train.
Q44 How many trailing zeros are in the number 5! (5 factorial)?
Q45: You have a 100 coins laying flat on a table, each with a head side and a tail side. 10 of them are heads up, 90 are tails up. You can’t feel, see or in any other way find out which 10 are heads up. Your goal: split the coins into two piles so there are the same number of heads-up coins in each pile.
Q46: If you have a square room with no roof, and you had four flagpoles you had to plant on the walls so that each flagpole touched two walls, how would you do it?
Q47: There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of its box. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly?
Q48: You have a 100 coins laying flat on a table, each with a head side and a tail side. 10 of them are heads up, 90 are tails up. You can’t feel, see or in any other way find out which 10 are heads up. Your goal: split the coins into two piles so there are the same number of heads-up coins in each pile.
Q49: There are 27 coins and a two-pan balance. All coins has same weight except for one, which is heavier than all others. All coins looks identical. What is the minimum number of weighing required to certainly find out heavier coin?
Q50: Two persons are walking into a railway tunnel. Upon crossing 2/3rd of the tunnel, they saw a train is coming from opposite direction. Each person ran for a different end of tunnel with speed of 10 km per hour. Fortunately, both persons escaped from the tunnel just right time i.e.. at the time train would have run through them. Assuming train was running with a constant speed and both persons reacted immediately, Find out speed of train.
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