# 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 $$\frac{1}{2}$$.

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) = $$\frac{2}{4} + \frac{1}{4}+ \frac{1}{4} = 1$$

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:

$1 - \frac{2}{9} = \frac{7}{9}$