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# Probability

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## Probability

**Probability is the 'chance' of something happening.**

It is almost certain to come up in your exam! (Nothing is ever completely certain!)

**Key points:**

**1.** We call 'something happening' an** event. **For example, getting a 6 with the roll of a dice.

**2.** Probability should always be written as a **fraction**, **decimal** or **percentage** never '1 in 10' or '3 chances out of 5'.

**3.** The probability of something happening must be between 0 and 1 (unlessyou are using percentage - 0 to 100).

**4.** The sum of the probabilities of every possible outcome is 1.

**5.** The probability of something **not happening **is 1 minus the probability of it happening.

**If we call a particular event 'A' then the probability of A happening is:**

**For example:**

p (getting an even number when you roll a dice) =

And p (**not **A) = 1 - p (A)

**For example:**

If p (rolling a 6 on a dice)

Then p (not rolling a 6)

In practice, a coin will not always land 'Heads' exactly half the times you throw it (although theoretically it should!).

If you do something a certain number of times and record the results you can write down **estimates** for the probabilities of each outcome.

These estimates are also known as **Relative Frequencies.**

**Here's an
example:**

A ball was drawn out of a bag containing coloured balls 200 times. Each time the ball was replaced. The results are shown below...

**Work out all the probabilities and write them in the boxes:**

You don't need to bother cancelling the fraction down to its simplest terms in this type of question. You will still get full marks.

**Why take the risk?**