The daily consumption of milk in a city, in excess of 20,000 litres, is approximately distributed as a gamma variate with parameters r = 2 and λ = 1/10,000. The city has a daily stock of 30,000 litres. What is the probability that the stock is insufficient on a particular day?
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Three technicians X, Y and Z service respectively 20%, 30% and 50% breakdowns when occur on an automated production line. The technician X makes an incomplete repair 1 time in 20, Y makes an incomplete repair 1 time in 10 and Z makes an incomplete 1 time in 15. For the next breakdown a repair made was found to be incomplete, find the probability that this repair was made by technician
(i) X,
(ii) Y, and
(iii) Z
State whether the following statements are True or False and also give the reason in support of your answer.
(a) If odds in favour of an event A are 2:5 then probability of happening of the event A will be .
(b) If two independent events A and B are such that A and B are independent. P(A) = and P(B) =
, then events A and
are independent.
c) If X is a discrete random variable with probability mass function (pmf)
| X | 0 | 1 | 2 |
| P[X=x] | 1 4 | 1 2 | a |
The probability that the dial will land somewhere between 0° and 90° will be .
The probability that a newly designed electronic component will survive a given shock test is 5/6. Find the probability that exactly 3 of the next 4 components tested survive.
Ms. X thinks that there is a 30% chance that her company will set up a branch office in New Delhi. If it is so, then she is 60% certain that she will be assigned the responsibilities of a branch manager there. What is the probability that Ms. X will be branch manager at the New Delhi office?
The probability that a person living in a certain city owns a dog is estimated to be 0.3. Find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog.
A company has installed 10,000 electric lamps in a metro. If these lamps have an average life of 1,000 burning hours with a S.D. of 200 hours. Assuming normality, what number of lamps might be expected to fail.
i) in the first 800 burning hours.
ii) between 800 and 1200 burning hours.
iii) more than 1000 burning hours
A bag contains 5 balls which are numbered from 1 to 5. Two balls are drawn without replacement from this. Find the expectation of the sum of the numbers on these balls.