Russian Roulette Riddle
You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?
Hint:
Russian Roulette
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Puzzle ID: #17681
Fun: *** (2.59)
Difficulty: ** (2.07)
Category: Probability
Submitted By: JMCLEOD****
Corrected By: cnmne
You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?
Answer
Label the chambers 1 through 6. Chambers 1 through 3 have bullets and chambers 4 through 6 are empty. After you spin the cylinder there are six possible outcomes:
1. Chamber 1 is fired first: Player 1 loses
2. Chamber 2 is fired first: Player 1 loses
3. Chamber 3 is fired first: Player 1 loses
4. Chamber 4 is fired first: Player 2 loses (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)
5. Chamber 5 is fired first: Player 1 loses (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)
6. Chamber 6 is fired first: Player 2 loses (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)
Therefore player 2 has an 4/6 or 2/3 chance of winning. Did you answer this riddle correctly?
YES NO
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
Puzzle ID: #17681
Fun: *** (2.59)
Difficulty: ** (2.07)
Category: Probability
Submitted By: JMCLEOD****
Corrected By: cnmne
You are in a game of Russian Roulette with a revolver that has 3 bullets placed in three consecutive chambers. The cylinder of the gun will be spun once at the beginning of the game. Then, the gun will be passed between two players until it fires. Would you prefer to go first or second?
Answer
Label the chambers 1 through 6. Chambers 1 through 3 have bullets and chambers 4 through 6 are empty. After you spin the cylinder there are six possible outcomes:
1. Chamber 1 is fired first: Player 1 loses
2. Chamber 2 is fired first: Player 1 loses
3. Chamber 3 is fired first: Player 1 loses
4. Chamber 4 is fired first: Player 2 loses (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)
5. Chamber 5 is fired first: Player 1 loses (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)
6. Chamber 6 is fired first: Player 2 loses (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)
Therefore player 2 has an 4/6 or 2/3 chance of winning. Did you answer this riddle correctly?
YES NO
The Traffic Light Riddle
There is a traffic light at the top of a hill. Cars can't see the light until they are 200 feet from the light.
The cycle of the traffic light is 30 seconds green, 5 seconds yellow and 20 seconds red.
A car is traveling 45 miles per hour up the hill.
What is the probability that the light will be yellow when the driver first crests the hill and that if the driver continues through the intersection at her present speed that she will run a red light?
The cycle of the traffic light is 30 seconds green, 5 seconds yellow and 20 seconds red.
A car is traveling 45 miles per hour up the hill.
What is the probability that the light will be yellow when the driver first crests the hill and that if the driver continues through the intersection at her present speed that she will run a red light?
Hint:
The probability of the driver encountering a yellow light and the light turning red before the car enters the intersection is about 5.5%.
At 45 mph the car is traveling at 66 feet/second and will take just over 3 seconds (3.03) to travel the 200 feet to the intersection. Any yellow light that is in the last 3.03 seconds of the light will cause the driver to run a red light.
The entire cycle of the light is 55 seconds. 3.03/55 = 5.5%. Did you answer this riddle correctly?
YES NO
At 45 mph the car is traveling at 66 feet/second and will take just over 3 seconds (3.03) to travel the 200 feet to the intersection. Any yellow light that is in the last 3.03 seconds of the light will cause the driver to run a red light.
The entire cycle of the light is 55 seconds. 3.03/55 = 5.5%. Did you answer this riddle correctly?
YES NO
Die Toss Riddle
If you toss a die and it comes up with the number one 9 times in a row, what is the probability that it will come up with one on the next throw?
Hint:
Pricey Teeth Riddle
Hint:
4 Prisoner Hat Riddle
As shown in picture above there are 4 men looking forward. None of them can see back. There is a opaque wall between man number 3 and man 4 (1,2,3 cannot see pass the wall). Two of the men are wearing a black hat and two of them are wearing a white hat. Each man can see the color of the hat wore by the men in front of him. (1 can see 2,3 and 2 can see 3) but each person does not know the color of the hat he is wearing.
Now one of the man needs to call out the color of his hat else they all die in 10 mins. Which man will callout the color of his hat correctly and why?
Now one of the man needs to call out the color of his hat else they all die in 10 mins. Which man will callout the color of his hat correctly and why?
Hint:
Answer is Man number 2.
Lets start by eliminating men. Man number 4 is at the other end of opaque wall facing other side. There is no way he can see any men or the color of their hat. So he is eliminated. Now man no 3 also cannot see anyone else - he cannot look back and he cannot see beyond wall. So he is eliminated too. Now man number 1 knows the color of man 2 and 3. Now lets say they (2 and 3) were wearing same color hat then man no 1 would know the color of his hat since there are 2 white and 2 black hat. But he keeps mum which means man 2 and 3 are wearing different hat. S0 man number 2 waits for sometime if he does not hear man 1 calling out that means man 2 and 3 are wearing different color hats. Since man 2 knows the color of hat wore by man 3 he know the color of his hat and calls it out. Did you answer this riddle correctly?
YES NO
Lets start by eliminating men. Man number 4 is at the other end of opaque wall facing other side. There is no way he can see any men or the color of their hat. So he is eliminated. Now man no 3 also cannot see anyone else - he cannot look back and he cannot see beyond wall. So he is eliminated too. Now man number 1 knows the color of man 2 and 3. Now lets say they (2 and 3) were wearing same color hat then man no 1 would know the color of his hat since there are 2 white and 2 black hat. But he keeps mum which means man 2 and 3 are wearing different hat. S0 man number 2 waits for sometime if he does not hear man 1 calling out that means man 2 and 3 are wearing different color hats. Since man 2 knows the color of hat wore by man 3 he know the color of his hat and calls it out. Did you answer this riddle correctly?
YES NO
Who Lives There?
Mr. Black lives in a black house, Mr. Brown lives in the brown house and Mr. Green lives in the green house. Who do you think lives in the white house?
Hint:
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You can see a beautiful red house on your left and a mesmeric green house on your right, a warming and attractive pink house on your front. Then where is the white house?
Hint:
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