Sum of probabilities

If you toss a coin, the probability of obtaining a head is \(\frac{1}{2}\) and the probability of obtaining a tail is also \(\frac{1}{2}\).

Two pound coins balancing on their side and two pound coins laid flat

P (head) + P (tail) = \(\frac{1}{2} + \frac{1}{2} = 1\)

If we choose a letter at random from the word 'SUMS', the probability of obtaining the letter 'S' is \(\frac{2}{4}\), the probability of obtaining the letter 'U' is \(\frac{1}{4}\), and the probability of obtaining the letter 'M' is \(\frac{1}{4}\).

P(S) + P(U) + P(M) = \(\frac{2}{4} + \frac{1}{4}+ \frac{1}{4} = 1\)

curriculum-key-fact
Remember that the sum of the probabilities of all possible outcomes is 1.
Question

The probability that I am late for work on any morning is \(\frac{2}{9}\). What is the probability that I am not late for work?

There are two possible outcomes - being late and not being late. The sum of their probabilities must add up to \(1\), so the probability of not being late is:

\[1 - \frac{2}{9} = \frac{7}{9}\]