The metro trains on a certain section run every 10 minutes between 5 a.m. to 10 p.m. What is the probability that a commuter entering the station at a random time during this period will have to wait
(i) at least five minutes?
(ii) zero minute?
(iii) 2 to 5 minutes?
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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 .
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.
The metro trains on a certain section run every 10 minutes between 5 a.m. to 10 p.m. What is the probability that a commuter entering the station at a random time during this period will have to wait
(i) at least five minutes?
(ii) zero minute?
(iii) 2 to 5 minutes?
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.
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 smoke-detector system uses two devices A and B. If smoke is present the probability that it will be detected by device A is 0.95; by device B, 0.98 and by both devices, 0.94. If smoke is present find the probability that it will be detected
A taxi cab company has 12 Ambassadors and 8 Fiats. If 5 of these taxi cabs are in the workshop for repair and an Ambassador is as likely to be in for repair as a Fiat, what is the probability that (i) 3 of them are Ambassadors and 2 are Fiats, (ii) at least 3 of them are Ambassadors, and (iii) all 5 are of the same make?