Two friends, two opinions

The idea

Judging how likely an event is from one's own interpretation of the available evidence, in words such as impossible, less likely, equally likely, more likely or certain, gives a subjective probability.

Same sky, two answers

One friend looks at the bright sun and says: "It is unlikely to rain today." Another feels the heat and says: "It could rain later." Both look at the same sky.

Can two sensible friends give different answers?

• Yes, if they read the evidence differently
• No, only one can be right

Choose a word

Choose a word for each event: impossible, less likely, equally likely, more likely or certain. Read the evidence after each choice.

A judgement

When we judge how likely an event is from our own reading of the evidence, using words like impossible, less likely, equally likely, more likely or certain, we give a subjective probability.

A die cannot show 7: the facts leave no room for opinion. But "will it rain today?" depends on how you read the weather, so two people may differ.

Notes

A subjective probability is a judgement of how likely an event is, in words such as impossible, less likely, equally likely, more likely or certain. It depends on how we read the evidence.

Check yourself

Which statement is a subjective probability?

Tossing a coin and getting heads. Which word fits best?

Two friends look at the same weather and give different words for rain. Is that possible?

Which word fits getting a number less than 7 on a die?

• "A die only has faces 1 to 6, so a 7 is impossible.". This follows from facts. Nobody can disagree with it.
• "The sun is shining, so I think rain is less likely." — correct. Yes. It comes from a person's own reading of the evidence.
• "All the sweets are red, so a red sweet is certain.". This follows from facts too.
• Impossible. Heads is one of the two results.
• Certain. Tails can also happen.
• Equally likely — correct. Yes. Heads and tails have the same chance.
• Yes. Each reads the evidence in their own way — correct. Yes. That is why this kind of probability is called subjective.
• No. The weather decides one right word for everyone. The weather decides what happens, but our words for how likely it is come from judgement.
• Yes, but only if one of them is guessing. Both can be careful and still read the clues differently.
• Impossible. Every face is less than 7, so it always happens.
• Certain — correct. Yes. Every face (1 to 6) is less than 7.
• Less likely. It happens on every roll, so it is certain.