Page 337 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Total Number of cases = 100

90
Required Probability = = 0.9
100
Example 7: What is the probability of getting a number greater than 4 with an ordinary die ?
Solution: Number greater than 4 in a die are 5 and 6.
∴ Number of favourable cases = 2
Total number of cases = 6

2 1
Required Probability = =
6 3
Example 8: Find the probability of drawing a face card in a single random draw from a well
shuffled pack of 52 cards.
Solution: There are 52 cards in a pack of cards.
Total number of cases = 52
Number of favourable cases (face cards include the Jack, Queen and King in each) = 12

12 3
Required Probability = =
52 13
Example 9: A card is drawn from an ordinary pack of playing cards and a person bets that it is a
spade or an ace. What are odds against his winning this bet ?
Solution: Total number of cases = 52
Since there are 13 spades and 3 aces (one ace is also present in spades), Therefore the
favourable cases = 13 + 3 = 16

16 4
The probability of winning the bet = =
52 13
4 9
The probability of losing the bet = 1 − =
13 13
9 4
Hence, odds against winning the bet = : = 9: 4
13 13
Example 10: A single letter is selected at random from the word ‘PROBABILITY’. What is the
probability that it is a vowel ?
Solution: There are 11 letters in the word ‘PROBABILITY’ out of which 1 is be selected.
∴ Total No. of words = 11
There are four vowels viz. O, A, I, I. Therefore favourable number of cases = 4

4
Hence, the required probability =
11
Example 11: Find the probability of drawing an ace from a set of 52 cards.
Solution: Number of exhaustive cases (n) = 52
There are 4 ace cards in an ordinary pack.
∴ Favourable cases (n) = 4
4 1
∴ Probability of getting an ace = =
52 13

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