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Maths

Probability

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Sum of probabilities

If you toss a coin, the probability of obtaining a head is 1/2 and the probability of obtaining a tail is also 1/2.

Front and back of a 1p coin

P(head) + P(tail) = 1 / 2 + 1 / 2 = 1

If we choose a letter at random from the word 'SUMS', the probability of obtaining the letter 'S' is 2 / 4, the probability of obtaining the letter 'U' is 1 / 4 and the probability of obtaining the letter 'M' is 1 / 4.

P(S) + P(U) + P(M) = 2 / 4 + 1 / 4+ 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 tomorrow is 2/9. What is the probability that I am not late for work?

Answer

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 - 2/9 = 7/9

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