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S1 – Probability Summary S1 – Probability Summary The probability of event A from n possible equally likely outcomes is P(A) = number of outcomes resulting in A n A A’ A B A The probability of event A from n possible equally likely outcomes is P(A) = number of outcomes resulting in A n A B P(A B) (A B) A AND B A OR B intersection of A & B union of A & B Two events are mutually exclusive if they cannot happen at the same time (do not overlap), e.g. A and A’. P(A’) = 1 – P(A) If events A and B are mutually exclusive then P(A B) = 0 The probability of event A OR B occurring is P(A B) = P(A) + P(B) – P(A B) Two events are exhaustive when it is certain that at least one of them occurs, e.g. A and A’. If events A and B are exhaustive then P(A B) = 1 Two events are independent if the outcome of one event has no possible influence on the outcome of the other (with replacement). If events A and B are independent then the probability of A AND B occurring is P(A B) = P(A) P(B). If event B is affected by the outcome of event A then A and B are dependent giving rise to conditional probability (without replacement). If events A and B are dependent then the probability that B occurs knowing that A has occurred is A’ = complement of A = NOT A P(BA) = P( A B) P( A) “probability of B given A” This is often rearranged to P(B A) = P(A) P(BA) If A and B are independent then P(BA) = P(BA’) = P(B) P(B A) = P(A) P(B) as we saw before. If A and B are dependent then P(BA) P(BA’). A tree diagram is a useful aid in calculating probabilities of several events. Remember to multiply along the branches and add between the branches. It will also shows dependency when calculating conditional probability. A’ A B A B P(A B) (A B) A AND B A OR B intersection of A & B union of A & B Two events are mutually exclusive if they cannot happen at the same time (do not overlap), e.g. A and A’. P(A’) = 1 – P(A) If events A and B are mutually exclusive then P(A B) = 0 The probability of event A OR B occurring is P(A B) = P(A) + P(B) – P(A B) Two events are exhaustive when it is certain that at least one of them occurs, e.g. A and A’. If events A and B are exhaustive then P(A B) = 1 Two events are independent if the outcome of one event has no possible influence on the outcome of the other (with replacement). If events A and B are independent then the probability of A AND B occurring is P(A B) = P(A) P(B). If event B is affected by the outcome of event A then A and B are dependent giving rise to conditional probability (without replacement). If events A and B are dependent then the probability that B occurs knowing that A has occurred is A’ = complement of A = NOT A P(BA) = P( A B) P( A) “probability of B given A” This is often rearranged to P(B A) = P(A) P(BA) If A and B are independent then P(BA) = P(BA’) = P(B) P(B A) = P(A) P(B) as we saw before. If A and B are dependent then P(BA) P(BA’). A tree diagram is a useful aid in calculating probabilities of several events. Remember to multiply along the branches and add between the branches. It will also shows dependency when calculating conditional probability.