### #1 - Probability Riddle Loaded Revolver

Henry has been caught stealing cattle, and is brought into town for justice. The judge is his ex-wife Gretchen, who wants to show him some sympathy, but the law clearly calls for two shots to be taken at Henry from close range. To make things a little better for Henry, Gretchen tells him she will place two bullets into a six-chambered revolver in successive order. She will spin the chamber, close it, and take one shot. If Henry is still alive, she will then either take another shot, or spin the chamber again before shooting.

Henry is a bit incredulous that his own ex-wife would carry out the punishment, and a bit sad that she was always such a rule follower. He steels himself as Gretchen loads the chambers, spins the revolver, and pulls the trigger. Whew! It was blank. Then Gretchen asks, 'Do you want me to pull the trigger again, or should I spin the chamber a second time before pulling the trigger?'

What should Henry choose?

Henry should have Gretchen pull the trigger again without spinning.

We know that the first chamber Gretchen fired was one of the four empty chambers. Since the bullets were placed in consecutive order, one of the empty chambers is followed by a bullet, and the other three empty chambers are followed by another empty chamber. So if Henry has Gretchen pull the trigger again, the probability that a bullet will be fired is 1/4.

If Gretchen spins the chamber again, the probability that she shoots Henry would be 2/6, or 1/3, since there are two possible bullets that would be in firing position out of the six possible chambers that would be in position.

### #2 - Monty Hall Problem Puzzle

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

You better switch!

Your first choice has a 1/3 chance of having the car, and that does not change.
The other two doors HAD a combined chance of 2/3, but now a Goat has ben revealed behind one, all the 2/3 chance is with the other door.

### #3 - Oracle Probability Interview Question

What is the probability of choosing the correct answer at random from the options below.

a) 1/4
b) 1/2
c) 1
d) 1/4

If the answer is 1/4, then because 2 out of 4 answer choices are '1/4', the answer must actually be 1/2. This is a contradiction. So the answer cannot be 1/4.
If the answer is 1/2 (or 1), then because 1/2 (or 1) is 1 out of 4 answer choices, the answer must be 1/4. This is again a contradiction. So the answer cannot be 1/2 (nor 1).

So none of the provided answer choices are correct. Therefore the probability of choosing the correct answer is 0%

### #4 - Tricky Probability Interview Puzzle

I have two coins.
* One of the coin is a faulty coin having tail on both side of it.
* The other coin is a perfect coin (heads on side and tail on other).

I blind fold myself and pick a coin and put the coin on table. The face of coin towards the sky is tail.

What is the probability that other side is also tail ?

2/3

2 possible scenario are :
case number side shown other side
1 A1 (H) A2 (H)
2 A2 (H) A1 (H)
3 B1 (H) B2 (T)
4 B2 (T) B1 (H)

case 4 is not possible so ans is 2/3

### #5 - Trick Probability Puzzle

What is the probability that you meet someone in your lifetime who is having an above average number of arms?

1) Impossible
2) Unlikely
3) Fifty Fifty
4) Fairly Likely
5) Certain

The probability is certain because the average is <2 arms.

### #6 - Famous Probability puzzle SHOOT

Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival?

He should shoot at the ground.

If Mr. Black shoots the ground, it is Mr. Gray's turn. Mr. Gray would rather shoot at Mr. White than Mr. Black, because he is better. If Mr. Gray kills Mr. White, it is just Mr. Black and Mr. Gray left, giving Mr. Black a fair chance of winning. If Mr. Gray does not kill Mr. White, it is Mr. White's turn. He would rather shoot at Mr. Gray and will definitely kill him. Even though it is now Mr. Black against Mr. White, Mr. Black has a better chance of winning than before.

### #7 - Ant Problem Probability Quiz

Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?

So let’s think this through. The ants can only avoid a collision if they all decide to move in the same direction (either clockwise or anti-clockwise). If the ants do not pick the same direction, there will definitely be a collision. Each ant has the option to either move clockwise or anti-clockwise. There is a one in two chance that an ant decides to pick a particular direction. Using simple probability calculations, we can determine the probability of no collision.

### #8 - Hard Logic Probabilty Puzzle

Bruna was first to arrive at a 100 seat theater.
She forgot her seat number and picks a random seat for herself.

After this, every single person who get to the theater sits on his seat if its available else chooses any available seat at random.
Neymar is last to enter the theater and 99 seats were occupied.

Whats the probability what Neymar gets to sit in his own seat ?

1/2

one of two is the possibility
1. If any of the first 99 people sit in neymar seat, neymar will not get to sit in his own seat.
2. If any of the first 99 people sit in Bruna's seat, neymar will get to sit in his seat.

### #9 - Monday Probability Problem

What is the probability of getting five Monday in a 31-days month ?

If a 31day month starts on a Saturday, Sunday or Monday it will have five Monday, if not it will have 4 Monday.
Probability is 3/7.

### #10 - Tough Probability Interview Question

There is a country where everyone wants a boy. Every family continue to have babies till a boy is born. If the probability of having a girl or a boy is the same, what is the proportion of boys to girls after some time in that country?

Since the probability of having a girl or a boy is same, half of the families will have a boy first and stop. The other half of the families will have a girl and from half of those families, the second born will be a boy and they will stop while the others will again have a girl. This process will continue.

Suppose the number of couples are N, the number of boys will be N.

1/2 have a boy and stop: 0 girls
1/4 have a girl, then a boy: N/4 girls
1/8 have 2 girls, then a boy: 2*N/8 girls
1/16 have 3 girls, then a boy: 3*N/16 girls
1/32 have 4 girls, then a boy: 4*N/32 girls

Total: N boys and
1N 2N 3N 4N
– + – + – + — +… = ~N

Therefore the proportion of boys to girl will be quite close to 1:1.