Mathematics : Probability

A committee of 3 persons is to be selected from amongst 4 men and 2 women. Find the probability, that the committee consists of:

(a) all 3 men           (b) 2 men and 1 woman               (c) 1 man and 2 women.

An urn contains 6 red, 4 blue and 5 black balls. 3 balls are drawn at random from the urn. Find the probability that:

(i) they are all of different colours            (ii) they are not all of different colours.

Check whether the following probabilities P(A) and P(B) are consistently defined :

(i) P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6

(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8 

Given  and  Find P(A or B), if A and B are mutually exclusive events.

Given  Find: P(neither A nor B), if A and B are mutually exclusive.

If E and F are events such that  Find: (i) P(E or F) (ii) P(not E and not F).

Events E and F are such that P(not E or not F) = 0.25. State whether E and F are mutually exclusive.

A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine:
(i) P(not A),      (ii)   P(not B)        (iii) P(Aor B)    (iv) P (not A and not B)   (v) P(not A or not B)

A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) = 0.35. Find: (i) P(A ∪ B) (ii) P(A' ∩ B') (iii) P(A ∩ B') (iv) P(B ∩ A')