Probability Tes...

Two buses A and B are scheduled to arrive at a town central bus station at noon. The probability that bus A will be late is 1/5. The probability that bus B will be late is 7/25. The probability that the bus B is late given that bus A is late is 9/10. Then the probabilities
(i) neither bus will be late on a particular day and
(ii) bus A is late given that bus B is late, are respectively

In a building programme the event that all the materials will be delivered at the correct time is $$M$$ and the event that the building programme will be completed on time is $$F.$$ Given that $$P(M) = 0.8$$ and $$P(M \cap F) = 0.65$$, find $$P(F/M).$$ If $$P(F) = 0.7$$, find the probability that the building programme will be completed on time if all the materials are not delivered at the correct time.

The value of $$P(S$$ or $$ T)$$ is:

Events S and T are

An urn contains 9 red, 7 white and 4 black balls A ball is drawn at random What is the probability that the ball drawn is not red ?

If only one hits the target, what is the probability that it is was the first man?

$$P[(\overline A\cap B)\cup (A \cap \overline B)]$$

Two dice are thrown. The probability that the sum of the numbers coming up on them is $$9$$, if it is known that the number $$5$$ always occurs on the first die, is

Suppose that of all used cars of a particular year 30% have bad brakes. You are considering buying a used car of that year. You take the car to a mechanic to have the brakes checked. The chance that the mechanic will give you the wrong report is 20%. Assuming that the car you take to the mechanic is selected at random from the population of cars of that year. The chance that the car's brakes are good, given that the mechanic says its brakes are good, is

If $$E$$ and $$F$$ are independent events such that $$P(E) = 0.7$$ and $$P(F) = 0.3$$, then P$$\displaystyle (E\cap F)$$