Long Answer TypeA 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.
Short Answer TypeAn 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
(i) P(A) = 0.5, P(B) = 0.7, 
Now, P(A) = 0.5 and 
which is not consistent.
Hence, the given probabilities are not consistently defined.
(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8
Now, P(A ∪ B) = 0.8 
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) 
0.8 = 0.5 + 0.4 - P(A ∩ B)
P(A ∩ B) = 0.1
P(A ∩ B) < P(A), P(A ∩ B) < P(B)
P(A ∩ B) > P(A), P(A ∪ B) > P(B)
Hence, the given probabilities are consistently defined.
Events E and F are such that P(not E or not F) = 0.25. State whether E and F are mutually exclusive.
Long Answer TypeA 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)
Short Answer TypeA 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')
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and 
Find P(A or B), if A and B are mutually exclusive events.
Find: P(neither A nor B), if A and B are mutually exclusive.
Find: (i) P(E or F) (ii) P(not E and not F).
