Page 268 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 12: Probability and Expected Value

14. A ................................. is an arrangement of a given set of objects in a definite order. Notes
(a) Permutation (b) Combination
(c) Arrangement (d) System
15. When no attention is given to the order of arrangement of the selected objects, we get a
.......................................
(a) Permutation (b) Combination

(c) Arrangement (d) System
16. A ................................ is the result of the simultaneous occurrence of two or more events.
(a) Event (b) Simple event
(c) Complex event (d) compound event

Case Study Independent Events

uppose a company hires both MBAs and non-MBAs for the same kind of managerial
task. After a period of employment some of each category are promoted and some
Sare not. Table below gives the proportion of company’s managers among the said
classes:

Academic Qualification
Promotional MBA Non - MBA Total
Status
(A) (A)

Promoted (B) 0.42 0.18 0 60
.
.
Not Promoted(B) 0.28 0.12 0 40
.
Total 0.70 0.30 100
Question
Calculate P(A/B) and P(B/A) and find out whether A and B are independent events.

12.4 Summary

1. (a) The number of permutations of n objects taking n at a time are n!
n ! n
(b) The number of permutations of n objects taking r at a time, are P r n r !
(c) The number of permutations of n objects in a circular order are (n - 1)!
(d) The number of permutations of n objects out of which n are alike, n are alike, ......
1 2
! n
n are alike, are
k
n
n 1 ! ! ... n k !
2
n ! n
(e) The number of combinations of n objects taking r at a time are C r
! r n r !
2. (a) The probability of occurrence of at least one of the two events A and B is given by:
P A  B P A P B P A  B 1 P A  B .
(b) The probability of occurrence of exactly one of the events A or B is given by:
P A  B P A  B or P A  B P A  B

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