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The Probability of Either One Event or Another

The Probability of Either One Event or Another

Sometimes there is more than one event together - combined probability. Here's an example:

This table is the probability of a book chosen at random falling into one of these three catagories.

The probability that a random book is either out on loan or on an unauthorised loan is:

P(L or U) = ^{44000 + 16000} ⁄ ₈₀₀₀₀
= ⁶⁰⁰⁰⁰ ⁄ ₈₀₀₀₀
= 0.75

This could also be written as:

P(L ∪ U) = ^{n(L ∪ U)} ⁄ _n(Ɛ)
= ^n(L) ⁄ _n(Ɛ) + ^n(U) ⁄ _n(Ɛ)
P(L ∪ U) = P(L) + P(U)

∪ is the union symbol which means 'or'. There is another symbol we'll look at later, ∩ which means 'and'. You can tell these apart by thinking fish n' chips = fish and chips - so the other one has to be or.

Find the probability that the next book chosen at random will be either out on loan or an adult non-fiction book.