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(BA) =
P( A  B)
P( A)
“probability of B given A”
 This is often rearranged to P(B  A) = P(A)  P(BA)
 If A and B are independent then
P(BA) = P(BA’) = P(B)  P(B  A) = P(A)  P(B) as we saw before.
 If A and B are dependent then P(BA)  P(BA’).
 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(BA) =
P( A  B)
P( A)
“probability of B given A”
 This is often rearranged to P(B  A) = P(A)  P(BA)
 If A and B are independent then
P(BA) = P(BA’) = P(B)  P(B  A) = P(A)  P(B) as we saw before.
 If A and B are dependent then P(BA)  P(BA’).
 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.