Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 9.19

Solution :
(i) Favourable cases^7 C 4 , Exhaustive cases^12 C 4

Probability

(^74)
(^124)

C 105 7

= C =495 33=

(ii) Favourable cases =^7 C 2 x^5 C 2
Exhaustive cases =^12 C 4

Probability

(^7252)
(^124)

C C 12 10 14

C 495 33

= × = × =

Example 27 :
A petrol pump proprietor sells on an average 80,000 worth of petrol on rainy days and an average of 95,000 on clear days. Statistics from the Metereological Department show that the probability is 0.76 for
clear weather and 0.24 for rainy weather on coming Monday. Find the expected value of petrol sale on
coming Monday.
Solution :
X 1 = 80,000; Pl = 0.24 X 2 = 95,000 P 2 = 0.76
The required probability = P 1 X 1 + P 2 X 2
= 0.24 X 80,000 + 0.76 X 95,000
= 19,200 + 72,200 = 91,400. The expected value of petrol sale on coming Monday = 91,400

Example 28 :
A bag contains 6 white and 9 black balls. Two drawings of 4 balls are made such that (a) the Balls are
replaced before the second trial (b) the balls are not replaced before the second trial. Find the probability
that the first drawing will give 4 white and the second 4 black balls in each case.

Solution:
(a) When the balls are replaced before the second trial the number of ways in which 4 balls may be drawn
is^15 C 4
The number of ways in which 4 white balls may be drawn =^6 C 4
The number of ways in which 4 black balls may be drawn =^9 C 4
Therefore, the probability of drawing 4 white balls at first trial

(^64)
(^154)

C 1

= C = 91

The Second trial of drawing 4 black balls.

(^94)
(^154)

C 9 8 7 6 4! 6

C 4! 15 14 13 12 65

= = × × × × =

× × ×