Page 279 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes
Example: Assuming that it is true that 2 in 10 industrial accidents are due to fatigue, find
the probability that:
1. Exactly 2 of 8 industrial accidents will be due to fatigue.
2. At least 2 of the 8 industrial accidents will be due to fatigue.
Solution:

Eight industrial accidents can be regarded as Bernoulli trials each with probability of success
2 1
p = = . The random variable r denotes the number of accidents due to fatigue.
10 5

2 6
1 4
8
1. P r 2 C 2 0.294
5 5
2. We have to find P(r 2). We can write
P(r 2) = 1 – P(0) – P(1), thus, we first find P(0) and P(1).
0 8
1 4
8
We have P 0 C 0 0.168
5 5
1 7
1 4
8
and P 1 C 1 0.336
5 5
P(r 2) = 1- 0.168 - 0.336 = 0.496
Example: The proportion of male and female students in a class is found to be 1 : 2. What
is the probability that out of 4 students selected at random with replacement, 2 or more will be
females?
Solution:
Let the selection of a female student be termed as a success. Since the selection of a student is
made with replacement, the selection of 4 students can be taken as 4 repeated trials each with
2
probability of success p .
3
Thus, P(r 2) = P(r = 2) + P(r = 3) +P(r = 4)

2 2 3 4
4 2 1 4 2 1 4 2 8
C 2 C 3 C 4
3 3 3 3 3 9
Note that P(r 2) can alternatively be found as 1 – P(0) – P(1)

Task The probability of a bomb hitting a target is 1/5. Two bombs are enough to destroy
a bridge. If six bombs are aimed at the bridge, find the probability that the bridge is
destroyed.

Example: An insurance salesman sells policies to 5 men all of identical age and good
health. According to the actuarial tables, the probability that a man of this particular age will be
alive 30 years hence is 2/3. Find the probability that 30 years hence (1) at least 1 man will be
alive, (2) at least 3 men will be alive.

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