If in a random experiment, there are n mutually exclusive and equally likely elementary events and
m of them are favourable to an event A, then the probability of p of happening of A, denoted by P(A),
is defined as the ratio (m/n).
The probability q of failure of event A is
Exhaustive events: The total number of possible outcomes of a random experiment is called exhaustive events.
(i) In tossing a coin, exhaustive events are two.
(ii) In throwing a die, the exhaustive number of cases is 6.
Mutually Exclusive: The events are said to be mutually exclusive if they can not occur simultaneously in a single draw.
When a coin is tossed, it can show either a head or a tail.
If we toss a tail, we can not get a head.
If we toss a head, we can not get a tail.
Thus these events are mutually exclusive.
The addition rule:
When two events are mutually exclusive, we can work out the probability of either of them occurring
by adding together the separate probabilities.
Multiplication Theorem of Probability:
If two events A and B are independent, then the probability that they will both occur is equal
to the product of their individual probabilities.
i.e., P(A and B) = P(A) × P(B)
In set notation: P(A ∩ B) = P(A) × P(B)
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