### Warm-up:

Probability Revision

(care of revisionmaths.com)

### The Problem:

Each working day, the probability of my leaving before 0800 was 0.25. Leaving after 0830 had a probability of 0.10. The probability of arriving late for a tutorial was dependent on my time of leaving home.

These probabilities are given in the following table:

Time I left my house | Before 0800 | Between 0800 - 0830 | After 0830 |
---|---|---|---|

Probability of being late | 0.01 | 0.09 | 0.9 |

I tutored 220 days in 2022. How many times was I late?

-/|\-

### Solution:

The solution is this is best found via a tree diagram.

$$P\left(\mathrm{late}\right)=0.151$$

So the number of times I was late equals $0.151\times 220=33.22$

Thirty three times late in a year is not good. I shall have to improve.

-oOo-

### Further Reading:

Probability Tree

(care of www.mathsgenie.co.uk)