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Mathematics · Data and probability

Probability of simple events

What are your chances of drawing a red marble from a bag? Learn to calculate probability when outcomes are equally likely, why probability lies between 0 and 1, impossible and certain events, and the "it either happens or it doesn't, so 50%" fallacy.

  • 20 min
  • 1 simulation
  • Mini quiz

Updated:

Preview

The question

In a class game, there are 3 red and 5 blue marbles in a bag. You will draw a marble with your eyes closed, and before you draw, you say a colour. If you guess right, you win a point. Which colour would you say? And can you express "how" lucky you are with a number?

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No account needed: change the values and check your answer. Some simulations ask for a prediction before they start; it doesn't matter whether it's right or wrong.

Ordering

Order the events by probability

Put the cards in order by dragging them or by swapping them with the arrows, then press Check.

Prediction

Predict first

Which is more likely: the dice showing 'an even number' or 'a number greater than 2'?

It doesn’t matter whether you’re right; the simulation opens once you choose.

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Frequently asked

5 questions

If something either happens or doesn't, isn't the probability 1/2?

No. Having two outcomes does not mean they are equally likely. If a bag has 1 red and 9 blue marbles, the result is either red or blue, but the probability of red is 1/10. The formula counts equally likely outcomes, not types of result.

With 3 red and 5 blue marbles, why isn't the probability of red 3/5?

The denominator must be the number of all outcomes. 3/5 compares the red marbles only with the blue ones, but there are 3 + 5 = 8 marbles you could draw. So the probability of red is 3/8.

Why can't a probability be greater than 1?

The favourable outcomes are part of all the outcomes, so s(A) can never be bigger than s(E). At most, every outcome is favourable; then the probability is 1 and the event is certain. If none are, the probability is 0 and the event is impossible.

How can I quickly find the probability that an event does not happen?

Subtract from 1, because P(A) + P(A') = 1. If 3 of the 8 equal sections of a spinner are yellow, the probability of not getting yellow is 1 − 3/8 = 5/8. This gives the same result as counting the 5 sections that are not yellow and dividing by 8.

If the probability of blue is 5/8, will exactly 5 of 8 draws be blue?

No. Even if you put the marble back each time, 5/8 tells you what to expect on average in the long run; it does not guarantee the result of any particular 8 draws. You might get 3 or 7 blue marbles in 8 draws. You will see this with experimental probability in the next lesson.