Paper 4: Fundamentals of Business Mathematics & Statistic

9.20 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Probability

Therefore the chance of the Compound event = =91 65 59151 6 6× =

(b) When the balls are not replaced :

At the first trial, 4 balls may be drawn in^15 C 4 ways and 4 white balls may be drawn in^6 C 4 ways.

Therefore the chance of 4 white balls at first trial

(^64)
(^154)

C 1

= C = 91 (as above)

When 4 white balls have been drawn and removed, the bag contains 2 white and 9 black balls.

Therefore at the second trial, 4 balls may be drawn in^9 C 4 ways and 4 black balls maybe drawn in^9 C 4 ways

So, the chance of 4 black balls at the second trial

(^94)
(^114)

C

C

9 8 7 6 4! 21

4! 11 10 9 8 55

=

= × × × × =

× × ×

Therefore the chance of the compound event =91 55 7151 21 3× =

Example 29 :

A salesman is known to sell a product in 3 out of 5 attempts while another salesman is 2 out of 5 attempts.

Find the probability that (i) No sale will be effected when they both try to sell the product and (ii) Either of

them will succeed in selling the product.

Solution :

Let the two salesmen be A and B.

P (A) = The probability that the salesman A is able to sell the

product =^35

P (B) = The probability that the salesman B is able to sell the product^25

(i) probability that no sale will be effected = 1 −^35            1 −2 65 25 =

(ii) probability that either of them will succeed in selling the product

3 2 3 2 19

= +5 5 5 5 25− × =