The probability that certain electronic component fail, when first used is 0.10. If it does not fail immediately, then the probability that it lasts for one year is 0.99. What is the probability that a new component will last for one year?

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2 then P(A')+P(B') is

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7 . The probability of passing at least one of them is 0.95. What is the probability of passing both ?

If the probabilities for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is

The probability that atleast one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate P(barA ) + P(barB) .

Two students Anil and Ashima appeared is an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability qualify the examination is 0.02. Find the probability that (a) Bothe Anil and Ashima will not qualify the examination. (b) Atleast one of them will qualify the examination and (c) Only one of them will qualify the examination.

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination is 0.02. Find the probability that (a) Both Anil and Ashima will not qualify the examination. (b) Atleast one of them will not qualify the examination and (c) Only one of them will qualify the examination.

One urn contains two black balls (labelled B_(1) and B_(2) ) and one white ball. A second urn contains one black ball and two white balls (labelled W_(1) , and W_(2) ). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball. (i) Write the sample space showing all possible outcomes (ii) What is the probability that two black balls are chosen ? (iii) What is the probability that two balls of opposite colour are chosen ?

Suppose A and B are two persons. The probability that A does the job is (4)/(5) and probability that B does the job is (3)/(4) . Then what is the probability that only one person does the job?

A small town has one fire engine and one ambulance available for emergencies. The probability that the fire engine is available when needed is 0.98 and the probability that the ambulance is available when called is 0.92. In the event of injury resulting from a building on fire, the probability that both the ambulance and the fire engine will be available is .........