Corollary
You are flipping a coin and wanting to find the probability of at least
one head or at least one tail. Now it is clear that the probability of
one coin flip landing heads is 1/2 and that of one coin flip landing tails
is also 1/2. Now these two events are mutually exclusive as you cannot
expect a coin land both heads and tails in one trial. Therefore you can
determine the required
probability by the mere addition of the two probabilities
: (or certainty).
Thus if A and B are two mutually exclusive events then
the probability that either A or B will happen is the sum of the
probabilities of A and B i.e. P (A + B) = P(A) + P(B)
Odds In Favor And Against
If P is the probability that an event will occur
and q (= 1  p) is the probability of the nonoccurrence of the event;
then we say that the odds in favor of the event occurring are p : q
(p to q) and the odds against its occurring are
q : p.
For example, if the event consists of drawing
a card if club from the deck of 52 cards, then the odds in favor are
Similarly the odds against a card of diamond
would be 3 : 1. The odds in favor of 4 or 6 in a
single toss of a fair die are
; i.e. 1 : 2 and the odds against are 2 : 1.
Multiplication Law of Probability
If there are two independent events; the respective
probability of which are known, then the probability that both will happen
is the product of the probabilities of their happening respectively P (AB)
= P (A) ´
P (B)
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