One card is drawn is drawn from a pack of 52 cards. Find the probability of getting :
(a) a red card  
(b) a jack of hearts
(c) a black face card
(d) a king.

2

(a)

A bag contain 2 red, 6 black and 8 green balls. A ball is drawn at random from the bag. Find the probabilty:
(a) a red ball
(b) a black ball
(c) a green ball
(d) a non-red ball

2

(a)

If E and F are two events such that \(P(E)=\frac { 1 }{ 4 } ,\) \(P(E)=\frac { 1 }{ 2 } \) and \( P(E\cap F)=\frac { 1 }{ 8 } \), find
(a) P(E or F)
(b) P(not E and not F).

2

(a)

If P(E) = \(\frac { 6 }{ 11 } \), P(F) = \(\frac { 5 }{ 11 } \) and P(E \(\cup\)F) = \(\frac { 7 }{ 11 } \) then find (a) P(E/F), (b) P(F/E)

2

(a)

If P(E) = \(\frac { 7 }{ 13 } \) , P(F) = \(\frac { 9 }{ 13 } \) and P(E\(\cap\)F) = \(\frac { 4 }{ 13 } \),then evaluate :
(a) \(P(\overline { E } /F)\)  
(b) \(P(\overline { E } /F)\)

2

(a)

If E and F be two events such that P(E) = \(\frac { 1 }{ 3 } ,P(F)=\frac { 1 }{ 4 } ,\) find \(P(E\cup F)\)  if E and F are independent events.

2

(a)

If P(F) = 0.35 and P(E\(\cup\)F) = 0.85 and E and F are independent events. Find P(E).

2

(a)

If P(F) =\(\frac { 1 }{ 2 } and\ P(F)=\frac { 1 }{ 5 } \) find \(P(\overline { E\cup F } )\) If E and F are independent events.

2

(a)

Prove that if E and F are independent events, then so are the events E and F′.

2

(a)

Three cards are drawn without replacement from a pack of 52 cards. Find the probability that 
(a) the cards drawn are king, queen and jack respectively.
(b) the cards drawn are king, queen and jack.

2

(a)

A box contains 50 bolts and 50 nuts. Half of the bolts and nuts are rusted. If two items are drawn with replacement, what is the probability that either both are rusted or both are bolts.

2

(a)

A couple has 2 children. Find the probability that both are boys, if it is known that (a) one of them is a boy (b) the older child is boys. 

2

(a)

If P(A)=\(\frac { 2 }{ 5 } ,P(B)=\frac { 1 }{ 3 } ,P(A\cap B)=\frac { 1 }{ 5 } ,\) then find \(P(\bar { A } /\bar { B } )\) .

2

(a)

If each element of a second order determinant is either 0 or 1, what is the probability that the value of determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value assumed with probability \(1\over2\)).

2

(a)