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Unit 27: Additive and Multiplicative Law of Probability

Notes
1
2
= 1 = 1
1 −
2
Thus it is certain that a head will ultimately appear if the coin is tossed indefinitely. The result holds
even if the coin is biased.
Incidentally, it is verified that P (S) = 1.
Note: In this example we find that though the number of points are infinite, these can be arranged
according to the sequence of natural numbers (such that there is one-one correspondence between
the natural numbers and the sample points); such an infinity of numbers is called denumerable infinity
(or countable infinity) of numbers.
Discrete Sample space

A sample space that consists of a finite number of sample points or a denumerably infinite number of
sample points is called a discrete sample space.
Self-Assessment

1. Tick the Correct Answer:
(i) Addition theorem states that if two events A and B are mutually exclusive, the probability of
occurrence of either A or B is given by:
(a) P (A) + P (B) (b) P (A) × P (B)
(c) P (A) – P (B) (d) P (A) × (B) – P (AB)
(ii) If two events A and B are independent, the probability that they will both occur is given by:
(a) P (A) + P (B) (b) P (A) × P (B)
(c) P (A) – P (B) (d) P (A) × (B) + P (AB)
(iii) If two events A and B are dependent, the conditional probability of B given A, i.e., P (B|A) is
calculated as:
(a) P (AB)|P (B) (b) P (A)|P (B)
(c) P (AB)|P (A) (d) P (A)|P (AB)
(iv) If two events A and B are dependent, the conditional probability of A given B, i.e., P (A|B) is
calculated as:
(a) P (B|A) (AB) (b) P (B)|P (A)
(c) P (AB)|P (A) (d) P (AB)|P (B)

(v) 5 C is equal to
2
(a)20 (b)10
(c)30 (d) 100
27.3 Summary

• It is easier to compute the probability of an event from known probabilities of other events.
This can be well observed if the given event can be represented as the union of two other
events or as the complement of an event.
• The probability of the conditional event is called conditional probability. For a conditional event,
instead of the whole sample space we have only the sample points comprising of the enent A,
i.e. the 6 sample points (5, 1), (5, 2), (5, 3), (5, 4), (5, 5) and (5, 6), and the conditional probability

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