# Popular Probability Puzzles

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

Puzzle #1: Chances of Having Same Birthday Problem

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

Puzzle #2: Chances Of Second Girl Child Problem

James and Calie are a married couple.
They have two children, one of the child is a boy. Assume that the probability of each gender is 1/2.
What is the probability that the other child is also a boy?

Puzzle #3: Pairs Of Blue, Brown And Black Socks

In your sock drawer, you have a ratio of 3 pairs of blue socks, 4 pairs of brown socks, and 5 pairs of black socks.
In complete darkness, how many socks would you need to pull out to get a matching pair of the same color?

Puzzle #4: 3 Baskets And 4 Balls Puzzle

You have 3 baskets & each one contains exactly 4 balls, each of which is of the same size. Each ball is either red, orange, white, or yellow, & there is one of each color in each basket.

If you were blindfolded, and balls are randomly distributed and then took 1 ball from each basket, what chance is there that you would have exactly 2 red balls?

Puzzle #5: Probability of a Car Passing By

The probability of a car passing a certain intersection in a 20 minute windows is 0.9. What is the probability of a car passing the intersection in a 5 minute window? (Assuming a constant probability throughout)

Puzzle #6: Red and Blue Marbles

You have 50 red marbles, 50 blue marbles and 2 jars. One of the jars is chosen at random and then one marble will be chosen from that jar at random. How would you maximize the chance of drawing a red marble? What is the probability of doing so? All 100 marbles should be placed in the jars.

Puzzle #7: Two Games in a Row

A certain mathematician, his wife, and their son all play a fair game of chess. One day when the son asked his father for 10 dollars for a Sunday night date, his father puffed his pipe for a moment and replied, “Let’s do it this way. Today is Thrusday. You will play a game of chess tonight, tomorrow, and a 3rd on Saturday. If you win two games in a row, you get the money.”

“Whom do I play first, you or mom?”

“You may have your choice,” said the mathematician, his eyes twinkling.

The son knew that his father played a stronger game than his mother. To maximize his chance of winning two games in succession, should he play father-mother-father or mother-father-mother?

Puzzle #8: Problem With Pearls

I’m a very rich man, so I’ve decided to give you some of my fortune. Do you see this bag? I have 1001 pearls inside it. 501 of them are white, and 500 of them are black. No, I am not racist. You are blind folded and I’ll let you take out any number of pearls from the bag. If you take out the same number of black and white pearls, I will reward you with a number of coins equivalent to the number of pearls you took.”

How many pearls should you take out to give yourself a good number of coins while still retaining a good chance of actually getting them?