#1 - Dice Sum Is 7 Probability Maths Puzzle

What is the probability of rolling a sum of 7 with two fair six-sided dice?

Dice Sum Is 7 Probability Maths Puzzle

0.1667 or 16.67%

When rolling two fair six-sided dice, there are a total of 36 possible outcomes (6 outcomes for the first die multiplied by 6 outcomes for the second die).

To calculate the probability of rolling a sum of 7, we need to determine the number of combinations that result in a sum of 7. These combinations are:

1 + 6
2 + 5
3 + 4
4 + 3
5 + 2
6 + 1

So, there are 6 favorable outcomes that result in a sum of 7.

The probability of rolling a sum of 7 is calculated by dividing the number of favorable outcomes by the total possible outcomes:

Probability = (Number of Favorable Outcomes) / (Total Possible Outcomes) = 6 / 36 = 1/6 ≈ 0.1667

Therefore, the probability of rolling a sum of 7 with two fair six-sided dice is approximately 0.1667 or 16.67%.

#2 - The Lottery Riddle

Chances of Mr. Button winning the local lottery in 8%. All participants lined up and Mr. Button is 3rd in the row. The first two participants lose the lottery.

What is the chance of Samuel Mr. Button now?

8%

The winning chance probability is still 8% as the outcome of Mr.Bitton winning the lottery is a separate event from rest losing the lottery.

#3 - Correct Dress Probability Problem

A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by one the girls come and pick a dress.
What is the probability that no girl will choose her own dress?

1/3

Explanation
Assuming D1 is the dress for Sister1, D2 is the dress for Sister2 and D3 is the dress for Sister3.

Therefore the total number of cases are illustrated below.

Sister1 Sister2 Sister3
D1 D2 D3
D1 D3 D2
D2 D1 D3
D2 D3 D1 ..... (1)
D3 D1 D2 .... (2)
D3 D2 D1

In both steps (1) & (2), no one gets the correct Dress.
Therefore probability that no sister gets the correct dress is 2/6 = 1/3

#4 - Hard Card Probability Riddle

A fresh card pile is taken out of a box (the pile has 54 cards including 2 jokers). One joker is taken out and then the cards are shuffled for a good amount of times. After shuffling, two piles are made by dividing that one pile.

What is the possibility that one of the piles will have a card sequence from A to K in order?

For x number of cards, the probability to obtain a precise sequence will be 1/x!

Here, we want 13 cards in sequence, which is why, x = 13

Therefore the possibility of obtaining a sequence from A to K in order = 1/6227020800

#5 - Dice Probability Sum Six

Can you calculate the probability of getting a sum of six when a dice is thrown twice?

Event = {(1,5) , (2,4), (3,3), (4,2), (5,1)}
Therefore, P (getting sum = 6) = 5/36

#6 - Dice Probability Riddle

Two men play a dice game involving roll of two standard dice. Man X says that a 12 will be rolled first. Man Y says that two consecutive 7s will be rolled first. The men keep rolling until one of them wins.

What is the probability that X will win ?

36/71

#7 - Chance Of Surviving Puzzle

Once upon a time there were three rivals who got together in a dark wood on an open spot for composing a quarrel by using guns. It was a kind of duel but there were three people in it and therefore it is a truel. There were A, B and C. there was some rules to be followed in the game. The rules of the games were:
-They have to draw the lots in order to find who will fire first and who will be second and who will be third.
- The next rule is that, they will start firing on each other unless there is a last person alive.
- Each person will decide on his own about which person he will fire on.
-it is quite clear that A hits and kills in all the shots and it is 100%. Whereas 80% of the shots are hit by B and C hits in 50% of the shots he tries to fire in. the three persons have their own strategy for firing. Nobody is killed by the stray bullet.

Question: who will have the highest chances for surviving in the truel and how much is the chance?

the person C will have the highest chances of survival.
Person A hits = 1
Person A misses = 0
Person B hits = 4/5
Person B misses = 1/5
Person C hits = 1/2
Person C misses = 1/2

#8 - James Bond Archer Of The Blind

James Bond is caught up in a mysterious scenario where the evil villain has him blindfolded. He somehow breaks through the handcuffs but is unable to get the blindfold off. Upon searching, he comes across a bow and 3 arrows. He can hear the villain speak, and thus tries to take a shot at him. He launches the first arrow, it misses the villain. He then launches the second arrow and it misses by a greater margin.

What is the probability that this third shot our james bond takes will be worse than the second shot?

2/3. How? Well, since he has 3 arrows, each shot has 1/3rd chance of being the best shot. So the chance that the third shot is not the best shot is 1 minus 1/3rd, thus 2/3rd.

#9 - Chances Of Survival Probability Puzzle

You are trapped into a death trap by the famous jigsaw killer. As usual, a screen flashes in front of you and explains you the trap game.

There are 100 pearls kept in a bowl in front of you and an empty bowl. Among the 100 pearls, 50 are white and 50 are black. You can divide them as you like into the two bowls. Once you are done, you will pull a lever, which will turn the room pitch black. The bowls will move and shuffle around. In the dark, you have to pick up one pearl from any bowl. Once you do that, the room will flood with lights again. If the peral you have in your hand is white, you will be allowed to live, but if the pearl you picked is black, the room will be filled with poisonous gas and you will die.

How will divide the pearls to increase your chances of survival?

For best probability of living, you must place one white pearl in a bowl and all the rest into another bowl.

This gives you a 1/2 probability of choosing a bowl which has just a white pearl. If you choose that, you will live.
If you choose another, you will still have an almost 1/2 probability of picking up a white pearl. (49 white pearls and 50 black pearls).

#10 - Probability Interview Gun Puzzle

You are stuck with a gangster who likes to play it rough. The only way to survive is to accept his invitation to play Russian Roulette.

He presents a revolver in which, three bullets have been placed consecutively. Now he spins the chamber cylinder of the gun. The cylinder wont be spun again. The gun will be passed between both of you till the gun fires and one of you is dead.

Will you prefer to go first or second if you are given a choice ?

2/3

Let us label the chambers for our convenience as C1, C2... C6.

Now, when the cylinder is spun, there can be the following six outcomes.
1. If C1 is fired first: Player 1 dies.
2. If C2 is fired first: Player 1 dies.
3. If C3 is fired first: Player 1 dies.
4. If C4 is fired first: Player 2 dies (First shot, player 1, C4 empty. Second shot player 2, C5, empty. Third shot player 1, C6 empty. Fourth shot player 2, C1 not empty.)
5. C5 is fired first: Player 1 dies (First shot, player 1, C5 empty. Second shot player 2, C6, empty. Third shot player 1, C1 not empty.)
6. C6 is fired first: Player 2 dies (First shot, player 1, C6 empty. Second shot, player 2, C1, not empty)

Therefore, if you choose to go second, you have a 4/6 or 2/3 chance of winning.