One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?
(i) E: ‘the card drawn is a spade’
F: ‘the card drawn is an ace’
(ii) E: ‘the card drawn is black’
F: ‘the card drawn is a king’
(iii) E: ‘the card drawn is a king or queen’
F: ‘the card drawn is a queen or jack’
Events A and B are such that `P(A) = 1/2, P(B) = 7/12 and P("not A or not B") = 1/4` . State whether A and B are independent?
If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability 1/2).
If A and B are two events such that `P(A) = 1/4, P(B) = 1/2 and and P(A ∩ B) = 1/8` , find P (not A and not B)
Two events A and B will be independent, if
(A) A and B are mutually exclusive
(B) P(A'B') = [1 - P(A)][1-P(B)]
(C) P(A) = P(B)
(D) P(A) + P(B) = 1