Gold and Silver Puzzle

At first, there was a 1/2 chance of picking from either bag. But when you picked out a gold coin, you got more information about which bag you probably picked from. Since 2 of the 3 gold coins were in the bag with 2 gold coins, there’s a 2 in 3 chance you picked from the bag with 2 gold coins. Therefore, there's a 2 in 3 chance that the other coin in that bag is also gold.

To learn more, read about Conditional Probability

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More Puzzles

You can buy a printable version of these puzzles.

Can you solve the baseball puzzle? A ball and a bat together cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?

There are three crates, one with apples, one with oranges and one with both apples and oranges mixed. Each crate is closed. They were labeled with one of three labels: “Apples”, “Oranges”, or “Apples and Oranges”, but a prankster came and switched all the labels.

If a card has a vowel on one side, then it has an even number on the other side. Which cards must be flipped to decide if this statement is true?

What is the shortest path for the spider to reach the fly?

In an alien species, every family keeps having children, one at a time, until they have one female child.

You have a stack of eight shuffled, face-down cards numbered 1 through 8. You turn over cards one at a time and get $100 for each card you turn over.

In a group of four people, what are the chances that two or more of them were born in the same month?

Even though driving at a higher speed increases the likelihood of a road collision, most collisions occur at moderate speeds. Why?

You have 50 red balls and 50 blue balls. You can distribute them between two boxes in any way you choose. Someone will come and pick a box at random, and then pick a ball from that box at random?

A wandering magician places a freshly shuffled deck face-down on a table. She then opens a small chest full of golden coins.

One of these boxes has a prize. I told Astrid only the color of the box. I told Bill only the symbol."

A tricky puzzle involving conditional probability. Which box should you pick from?

There are 11 gumballs in a machine: 6 pink, 4 white, and 1 blue. They cost 10 cents each. You want 2 of the same colour (any colour will do), but they come out at random.

Two boys on bicycles 20 miles apart began racing directly toward each other. The instant they started, a fly on the handle of one bicycle started flying straight toward the other cyclist.

Every day you flip a fair coin until you get heads, then stop. What’s the long-run average number of flips you make per day?

Your friend puts three dice on the table with unusual numbers on their sides. Your friend then suggests a game.

Highly intelligent children tend to have friends who are less intelligent than they are. What is the most likely explanation for this?

You post a survey asking, 'Do you like surveys?' 100 people fill out the survey. 95 of them answer 'Yes'. Can you conclude that most people like surveys?

You have 5 bottles, each containing 10 pills. One of them has heavier pills. Can you find out which one?

Jack is looking at Anne. Anne is looking at George. Jack is married and George is not married. Is a married person looking at an unmarried person?

You wrap a band around the equator so that it touches the ground at all places. Then you add 10 meters to its length. How far will it rise above the ground?

You are standing at the South Pole. You walk 1 kilometer north. You turn 90 degrees and walk in a line. Will you ever reach the South Pole again?

You have 100 kg of potatoes that are 99% water by weight. They dehydrate, and now they are 98% water by weight. How much do they weigh now?

You are on a game show. You have to choose between one of three doors. Behind one of them is a prize; behind the other two, nothing.

Can you solve the coin flip puzzle? If you toss a coin 4 times, what is the most likely split between heads and tails?

Draw 2 squares inside this square to isolate all the dogs from each other.

There are three candidates in an election: A, B, and C. Most voters prefer A over B. Most voters prefer B over C. Can we conclude that most voters prefer A over C?

You are blindfolded and there are four coins in front of you. You know that two of them are heads side up and two of them are tails side up.

Binary Labs makes only two kinds of robots: truth-bots, which only tell the truth, and trick-bots, which only lie. They look identical.

You have four cookies. One of them turns mice pink an hour after they eat even one bite, but you don’t know which one! You need to figure it out in an hour.

Can you solve this math puzzle? Look at the picture and determine how much an empty jar weighs. There are multiple ways to solve this.

Three smart boys are standing in a line. Each is wearing a hat that is either red or blue, but they don’t know the color of their own hat.

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Statistical Shenanigans Worksheets and Lesson Plans

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