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# Probability and Expectations

### Probability and Expectations

We can use probability to estimate how many times an event will happen in the future.

Probability tells us the chance of an event happening. We can use probability to find an estimate of how often an event will happen again in the future.

Using probability this way is only ever an **estimate** as probability is only theoretical. However, it is likely that if an event was continued a high to infinite number of times, it would approach the estimate of the probability.

Tom rolls a standard and fair 6-sided die 300 times. How many times can we expect him to land on a six?

What is the probability of landing on a six if he just rolls the die once?

The probability is $\dfrac{1}{6}$.

This means that in every 6 rolls, we expect 1 of the rolls to land on a six.

Multiply this by the total number of rolls

$\dfrac{1}{6} \times300 = 50$.

Great work! 🙌

So in 300 rolls, we expect it to land on a six 50 times

Grace rolls a standard 6-sided die 120 times. How many times can she expect to land on a four?