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Probability Pattern

581

Place a few balls in the tube and watch carefully the paths they take through the pipe maze, and how that affects which of the big tubes the balls end up in. Can you guess where the ball will land? Which tube is the ball most likely to land in?

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Forces Maths
There is an air stream in the tube, powered by a fan. It is like a vacuum cleaner set on blow rather than suck. When a ball is placed in the tube, it is carried by the air stream to the top. As the ball goes up the tube it gains enough energy to pass round the loop. It then drops into the top of the maze. The ball will then travel through the maze of small pipes at the top of the structure and drops into one of the 7 large tubes at the bottom of each possible path. Why do far more balls end up in the middle 3 tubes than the end tubes?
Solution

Why do more balls end up in the centre?

Reveal

Each time a ball arrives at a junction in the maze, there is an equal chance (1 in 2) of it bouncing right or left. There is the same chance (or probability) as flipping a coin and getting a head or a tail. There is an equal chance of getting either.

This exhibit has seven possible outcomes. For a ball to land in leftmost tube it has to go left six times through the pipe maze. Similarly, there’s only one way a ball can get to the rightmost tube. The reason why more balls end up in the middle is because there are more paths the balls can take to the middle. There are twenty different paths a ball can take to get to the middle, for instance, it could go left three times, then right three times. What other ways can you think of for the ball to get to the middle tube? Since there are twenty different paths and each path is equally likely, you would expect to see twenty times as many balls in the middle tube as you do in one of the tubes on the end.

On average if you place 64 balls into the maze one will fall into each of the end tubes and twenty will fall into the tube in the centre.

What is Probability?

Even though the path of an individual ball is completely unpredictable, the average number of balls that fall into the tubes at the bottom makes a clearly repeatable pattern called a Bell Curve (or Normal Distribution). This is the basis of the branch of mathematics called probability.

Try this

Things you can try yourself

Try flipping coins. Can you predict whether you will get heads or tails with each throw? What is the highest number of heads you can throw in a row? If you flipped the coin a million times, you would have a 38% chance of seeing 20 heads in a row.

Pascal's Triangle

The exact odds of a ball landing in each of the tubes can easily be calculated using Pascal’s Triangle.

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Welcome to Look Closer, Techniquest's brand new digital tool. We're trialling Look Closer as a way of offering you a closer look at the science demonstrated by many of our exhibits. You'll find visitor sheets, videos, articles on contemporary science as well as fun trails to navigate your way around the exhibition space.

Speak to our Science Communicators to find out more.