Mathematics · 20 minutes

Let evidence change your mind

Both bags can produce either colour. One draw matters, but it cannot reveal the hidden bag with certainty.

Keep this question in mindHow much should evidence change what we believe?

Notice the problem

Each clue moves belief by a measured amount.

Red is possible from both bags, but it is four times more likely from one of them.

A hidden causeEach clue moves belief by a measured amount.

Red is possible from both bags, but it is four times more likely from one of them.

Three things to notice

Look at these three ideas.

Each picture shows one part of the question. You will test the ideas next.

Start with possible explanations

Before drawing, either hidden bag is equally possible, so each begins at 50 percent.

Ask how expected the clue was

A red draw supports the red-heavy bag because red is more likely there.

Update, then stay open to more evidence

A run of clues can build strong support, but rare results remain possible.

Your prediction

You draw one red counter. What should happen to your belief that the hidden bag is red-heavy?

Choose what you think will happen. It is fine to be wrong. The experiment will help you find out.

AIt should increase, but not reach certaintyEither bag can produce red, but one makes red more often.BIt should become 100 percent certainOne red counter proves that the bag is red-heavy.CIt should stay at 50 percentOne result cannot count as evidence.DIt should decreaseA red counter supports the blue-heavy bag more.

Why do you think so? One clear sentence is enough.

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