Probability Distributions

Question 1

Multiple choice

A man and a woman appear for two vacancies for the same post. The probability of the man's selection is 1/4 and that of the woman's is 1/3. The probability that none of them will get selected is

1/2
1/3
1/4
1/5
-

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Answer

$\frac{6}{32}$

Answer

0.45, 0.30 and 0.25

Answer

None of these

Answer

$\frac{7}{20}$

Answer

t_e = $\frac{t_o + 4t_1 + t_p}{6}$

Answer

$\lambda e^{-\lambda t}$

Question 2

Multiple choice

The odd against a certain event is 5/2 and the odds in favour of another independent event is 6/5. The probability that none of the events will occur is

6/11
5/11
52/77
25/77
-

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Question 3

Multiple choice

In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most on negative value in five trails is

$\frac{1}{32}$
$\frac{2}{32}$
$\frac{3}{32}$

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Question 4

Multiple choice

An automobile plant contracted to buy shock absorbers from two suppliers X and Y. x supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. the ones that pass the quality test are considered reliable. Of X' shock absorbers, 96% are reliable, of Y's shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

0.288
0.334
0.667
0.720

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Question 5

Multiple choice

A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would be

0.45, 0.25 and 0.30
0.45, 0.55 and 0.00
0.45, 0.35 and 0.20

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Question 6

Multiple choice

If probability density function of a random variable X is f(x) = x² for – 1^_$\le$x^_$\le$1, and = 0 for any other value of x Then, the percentage probability ^{$p \left(}

\dfrac{1}{3} \le x \le \dfrac{1}{3} \right) $is

0.247
2.47
24.7
247

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Question 7

Multiple choice

A hydraulic structure has four gates which operate independently. The probability of failure of each gate is 0.2. Given that gate I has failed, the probability that both gates 2 and 3 will fail is

0.240
0.200
0.040
0.008

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Question 8

Multiple choice

A box contains 10 screws, 3 of which are defective. Two screws are drawn at random with replacement. The probability that none of the two screws is defective will be

100%
50%
49%

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Question 9

Multiple choice

A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and 1/6, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

1 and 1/3
1/3 and 1
1 and 4/3
1/3 and 4/3

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Question 10

Multiple choice

A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is

$\frac{42}{125}$
$\frac{25}{29}$
$\frac{5}{9}$

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Question 11

Multiple choice

The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is

0.029
0.034
0.039
0.044

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Question 12

Multiple choice

An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X's shock absorbers, 96% are reliable. Of Y's shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

0.288
0.334
0.667
0.720

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Question 13

Multiple choice

The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is

Normal
Poisson
Erlang
Beta

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Question 14

Multiple choice

The expected time (t_e) of a PERT activity in terms of optimistic time (t₀), pessimistic time (t_p) and most Likely time (t_l) is given by

t_e = $\frac{t_o + 4t_p + t_{p1}}{6}$
t_e = $\frac{t_o + 4t_1 + t_p}{3}$
t_e = $\frac{t_o + 4t_1 + t_1}{3}$

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Question 15

Multiple choice

In an M/M1 queuing system, the number of arrivals in an interval of length T is a Poisson random variable (i.e the probability of there being n arrivals in an interval of length T is $\frac{e^{-\lambda T(\lambda T)^n}}{n!}$) . The probability density function f(t) of the inter-arrival time is given by

$\lambda^2\bigg(e^{-\lambda^2t}\bigg)$
$\frac{e^{-\lambda^2t}}{\lambda^2}$
$\frac{e^{-\lambda^2t}}{\lambda}$

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Probability Distributions

Probability Distributions Questions