Page 336 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 26: Theory of Probability: Introduction and Uses

Notes
m 1
∴ P(H) = =
n 2
Example 2: What is the probability of getting an even number in a throw of an unbiased die ?
Solution: When a die is tossed, there are 6 equally likely cases, i.e., 1, 2, 3, 4, 5, 6.
Total number of equally likely cases = n = 6
Number of cases favourable to even points (2, 4, 6) = m = 3

3 1
∴ Probability of getting an even number = =
6 2
Example 3: What is the probability of getting a king in a draw from a pack of cards ?
Solution: Number of exhaustive cases = n = 52
There are 4 king cards in an ordinary pack.
∴ Number of favourable cases = m = 4

4 1
∴ Probability of getting a king = =
52 13
Example 4: From a bag containing 5 red and 4 black balls. A ball is drawn at random. What is the
probability that it is a red ball ?
Solution: Total No. of balls in the bag = 5 + 4 = 9
No. of red balls in the bag = 5

5
∴ Probability of getting a red ball =
9
Example 5: A bag contains 5 black and 10 white balls. What is the probability of drawing (i) a
black ball, (ii) a white ball ?
Solution: Total number of balls = 5 + 10 = 15
No. of black balls 5 1
(i) P (black ball) = = =
Total No. of balls 15 3

No. of white balls 10 2
(ii) P (white ball) = = =
Total No. of balls 15 3
Example 6: In a lottery, there are 10 prizes and 90 blanks. If a person holds one ticket, what are the
chances of
(i) getting a prize
(ii) not getting a prize
Solution: Total No. of tickets = 10 + 90 = 100
(i) Probability of getting a prize:
No. of prizes = 10
∴ No. of favourable cases = 10
Total No. of cases = 100
10 1
Required Probability = = = 0.1
100 10
(ii) The probability of not getting a prize:
No. of Blanks = 90
∴ Number of favourable cases = 90

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