The 100 Seat Airplane
People are waiting in line to board a 100-seat airplane. Steve is the first person in the line. He gets on the plane but suddenly can't remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it's available, otherwise they will choose an open seat at random to sit in.
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?
Hint: You don't need to use complex math to solve this riddle. Consider these two questions:
What happens if somebody sits in your seat?
What happens if somebody sits in Steve's assigned seat?
The correct answer is 1/2.
The chase that the first person in line takes your seat is equal to the chance that he takes his own seat. If he takes his own seat initially then you have a 100% chance of sitting in your seat, if he takes your seat you have a 0 percent chance. Now after the first person has picked a seat, the second person will enter the plan and, if the first person has sat in his seat, he will pick randomly, and again, the chance that he picks your seat is equal to the chance he picks someone your seat. The motion will continue until someone sits in the first persons seat, at this point the remaining people standing in line which each be able to sit in their own seats. Well how does that probability look in equation form? (2/100) * 50% + (98/100) * ( (2/98) * 50% + (96/98) * ( (2/96) * (50%) +... (2/2) * (50%) ) ) This expansion reduces to 1/2.
An easy way to see this is trying the problem with a 3 or 4 person scenario (pretend its a car). Both scenarios have probabilities of 1/2. Did you answer this riddle correctly?
YES NO
The chase that the first person in line takes your seat is equal to the chance that he takes his own seat. If he takes his own seat initially then you have a 100% chance of sitting in your seat, if he takes your seat you have a 0 percent chance. Now after the first person has picked a seat, the second person will enter the plan and, if the first person has sat in his seat, he will pick randomly, and again, the chance that he picks your seat is equal to the chance he picks someone your seat. The motion will continue until someone sits in the first persons seat, at this point the remaining people standing in line which each be able to sit in their own seats. Well how does that probability look in equation form? (2/100) * 50% + (98/100) * ( (2/98) * 50% + (96/98) * ( (2/96) * (50%) +... (2/2) * (50%) ) ) This expansion reduces to 1/2.
An easy way to see this is trying the problem with a 3 or 4 person scenario (pretend its a car). Both scenarios have probabilities of 1/2. Did you answer this riddle correctly?
YES NO
I Live In The Ocean Riddle
I live in the ocean.
I swim wherever I want.
I sing to my family.
I can breathe through a hole in the top of my head.
What am I?
I swim wherever I want.
I sing to my family.
I can breathe through a hole in the top of my head.
What am I?
Hint:
Seabed Eels Riddle
Hint:
A Goat At Sea
Hint:
Seasick Auctions Riddle
Hint:
One is the effects of a sail and the other is a sale of effects. Did you answer this riddle correctly?
YES NO
YES NO
Stones In The Sea Riddle
Hint:
Between Land, Sea The The Sky
Im always there, some distance away. Somewhere between land or sea and sky I lay. You may move towards me, yet distant I stay.
Hint:
Trampoline Season Riddle
Hint:
The Cutest Season Riddle
Hint:
Favorite Season Riddle
Hint:
Sea Sand Riddle
Hint:
Floating In The Sea
Hint:
More Lives Than A Cat
Hint:
Kill Me And I Shall Live
Hint:
Sea Dragon Meals Riddle
Hint:
Add Your Riddle Here
Have some tricky riddles of your own? Leave them below for our users to try and solve.