How many times was I late?

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 (late) = 0.25 \times 0.01 + 0.65 \times 0.09 + 0.10 \times 0.90

$P (late) = 0.151$
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-

Warm-up:

The Problem:

Solution:

Further Reading: