The events A and B are mutually exclusive so:
|A||P(A or B) = P(A) +(B)|
|B||P(A and B)=P(A)x P(B)|
|C||P(A) = P(B)|
|D||P(A) + P(B) = 1|
PROBABILITY & PROBABILITY DISTRIBUTIONS
a. The probability of an event is a quantitative measure of the proportion of all possible, equally likely outcomes that are favourable to the event; it is denoted by p.
b. Probabilities are usually expressed as decimal fractions, not as a percentages, and must lie between zero(zero probability) and one(absolute certainity).
c. The probability of an event cannot be negative.
d. Probability of an event can be expressed as a ratio of the number of likely outcomes to the number of possible outcomes.
e. The probability of an event not occurring is equal to one minus the probability that it will occur; this is denoted by q.
Mutually Exclusive Events & the Addition Rule
Two events are said to be mutually exclusive when the occurrence of one precludes the occurrence of the other, eg - male or female, pregnant or not, blood group A or O etc.
The probability of mutually exclusive events occurring is the probability that either one event occurs or the other event occurs. Thus the probability of being either blood type A or blood type O is:
P (O or A) = P (O) +P (A)
Independent events & the multiplicative rule
Two different events are independent if the outcome or occurrence of one event has no effect on the outcome or occurrence of the second event. Eg – gender and blood types are independent events; the sex of the person doesn’t affect in any way the person’s blood type.
The probability of two independent events is the probability that both events occur, and this probability is found by multiplying the probabilities of the two events. Thus:
P (male and blood type O) = P (male) x P (blood type O).