Page 123 - DMTH404_STATISTICS

Unit 7: Modern Approach to Probability

3. (a) The probability of simultaneous occurrence of the two events A and B is given by: Notes
P (A  ) B  P ( ) ( /A .P B A ) or  P ( ) ( /B .P A ) B
If A and B are independent P A B b

(b) g b g.
P A P B b g .
4. Bayes Theorem :
P ( ) ( /A .P D A )
n
P (A k /D )  n k k , (k  1,2, ...... )
å P ( ) ( /A i .P D A i )
i 1
Here A , A , ...... A are n mutually exclusive and exhaustive events.
1 2 n
7.5 Keywords

Mutually exclusive outcomes: Two or more outcomes of an experiment are said to be mutually
exclusive if the occurrence of one of them precludes the occurrence of all others in the same trial
i.e. they cannot occur jointly. For example, the two possible outcomes of toss of a coin are
mutually exclusive. Similarly, the occurrences of the numbers 1, 2, 3, 4, 5, 6 in the roll of a six
faced die are mutually exclusive.

Exhaustive outcomes: It is the totality of all possible outcomes of a random experiment. The
number of exhaustive outcomes in the roll of a die are six. Similarly, there are 52 exhaustive
outcomes in the experiment of drawing a card from a pack of 52 cards.

7.6 Self Assessment

Choose the appropriate answer:
1. Two cards are drawn successively without replacement from a well-shuffled pack of 52
cards. The probability that one of them is king and the other is queen is

8 4 1
(a) (b) (c) (d) none of these.
13 51 13 51 13 17
´
´
´
2. Two unbiased dice are rolled. The chance of obtaining an even sum is
1 1 1
(a) (b) (c) (d) none of these.
4 2 3
3. Two unbiased dice are rolled. The chance of obtaining a six only on the second die is
5 1 1
(a) (b) (c) (d) none of these.
6 6 4
4
4. If P A a f = , then odds against A are
5
(a) 1 : 4 (b) 5 : 4 (c) 4 : 5 (d) none of these.
5. The probability of occurrence of an event A is 0.60 and that of B is 0.25. If A and B are
mutually exclusive events, then the probability of occurrence of neither of them is
(a) 0.35 (b) 0.75 (c) 0.15 (d) none of these.
6. The probability of getting at least one head in 3 throws of an unbiased coin is

1 7 3
(a) (b) (c) (d) none of these.
8 8 8

LOVELY PROFESSIONAL UNIVERSITY 115