The probability that student selected at random from a class will pass in Mathematics is \(\frac { 2 }{ 3 } \) and the probability that he passes in Mathematics and English is \(\frac { 1 }{ 3 } \). What is the probability that he will pass in English if it is known that he has passed in Mathematics?

Events A and B are such that P(A) = \(\frac { 1 }{ 2 } \) , P(B) = \(\frac { 7 }{ 12 } \) and P(not A or not B) = \(\frac { 1 }{ 4 } \). State whether A and B are independent? 

Given that the events A and B are such that P(A) = \(\frac { 1 }{ 2 } \), P(AUB) = \(\frac { 3 }{ 5 } \) and P(B) = p. find P if they are mutually exclusive events. 

An experiment has the four possible mutually exclusive outcomes A, B, C and D, Check whether the following assignments of probability are permissible.
p(A) = 0.32, P(B) = 0.28, P(C) = - 0.06, P(D) = 0.46

If A and B are two events such that \(P(A\cup B)=0.7 ,\) \(P(A\cap B)=0.2\) ,\(P(\bar { B } )=0.5,\) show that A and B are independent.