If P(A) = 0.5, P(B) = 0.8 and P(B/A) = 0.8, find P(A/B) and P(A\(\cup \)B)

If A and B are two independent events such that P(A\(\cup \)B) = 0.6, P(A) = 0.2,  find P(B).

If for two events A and B, P(A) = \(\frac{3}{4}\), P(B) = \(\frac{2}{5}\) and A\(\cup \)B = S (sample space), find the conditional probability P(A/B).

The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15.
(i) If the oil had to be changed, what is the probability that a new oil filter is needed?
(ii) If a new oil filter is needed, what is the probability that the oil has to be changed?

Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.

Given P(A) = 0.4 and P(A\(\cup \)B)=0.7. Find P(B) if
(i) A and B are mutually exclusive
(ii) A and B are independent events
(iii) P(A / B) = 0.4
(iv) P(B / A) = 0.5

An integer is chosen at random from the first ten positive integers. Find the probability that it is (i) an even number (ii) multiple of three.

A die is rolled. If it shows an odd number, then find the probability of getting 5.

Three coins are tossed simultaneously, what is the probability of getting i) exactly one head ii) at least one head iii) at most one head?

If A and B are two independent events such that, P(A) = 0.4 and P\((A\cup B)\) = 0.9. Find P(B).