FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 9.5(b) The number of ways of drawing a king and a queen = 4× 4
The required probability
4 4 6
26 51 663
= × =
×
(c) Two kings can be drawn out of 4 kings in^4 C 2 =4 2. 2 2. 2 2 ×1× 2 ×1-^4 =^4 =4 ×3×2×1=6ways
The probability of drawing 2 kings
6 1
=26 51 221× =
Example 5 :
A bag contains 7 red, 12 white and 4 green balls. What is the probability that :
(a) 3 balls drawn are all white and
(b) 3 balls drawn are one of each colour?
Solution :
(a) Total number of balls
= 7 +12 + 4 = 23
Number of possible ways of drawing 3 out of 12 white
=^12 C 3
Total number of possible ways of drawing 3 out of 23 balls
=^23 C 3
Therefore, probability of drawing 3 white balls(^123)
(^233)
C 220
= C = 1771 = 0.1242
(b) Number of possible ways of drawing 1 out of 7 red —^7 C 1 Number of possible ways of drawing 1 out of
12 white =^12 C 1 Number of possible ways of drawing 1 out of 4 green -^4 C 1
Therefore the probability of drawing balls of different colours
(^7112141)
(^233)
C C C 7 12 4
C 1771
= × × = × ×
= 0.1897
9.3.2. Relative Frequency Theory of probability :
Classical approach is useful for solving problems involving game of chances—throwing dice, coins, etc.
but if applied to other types of problems it does not provide answers. For instance, if a man jumps from a
height of 300 feet, the probability of his survival will, not be 50%, since survival and death are not equally
alike.
Similarly, the prices of shares of a Joint Stock Company have three alternatives i.e. the prices may remain
constant or prices may go up or prices may go down. Thus, the classical approach fails to answe questions
of these type.
If we toss a coin 20 times, the classical probability suggests that we; should have heads ten times. But in
practice it may not be so. These empirical approach suggests, that if a coin is tossed a large number of
time, say, 1,000 times, we can expect 50% heads and 50% tails. Vor Miscs explained, “If the experiment be