Let A and B be two events such that \(P(\overline{A\cup B})={1\over6}, P(A\cap B)={1\over4}\) and \({P(\overline{A})}={1\over4}\). Then the events A and B are

(a)

Equally likely but not independent

(b)

Independent but not equally likely

(c)

Independent and equally likely

(d)

Mutually inclusive and dependent

A man has 3 fifty rupee notes, 4 hundred rupees notes, and 6 five hundred rupees notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination?

(a)

1:12

(b)

12:1

(c)

13:1

(d)

1:13

If A and B are two events such that A ⊂ B and P(B)\(\neq o\), then which of the following is correct?

(a)

\(P(A/B)={P(A)\over P(B)}\)

(b)

P(A/B)

(c)

P(A/B)\(\ge\)P(A)

(d)

P(A/B)>P(B)

If X and Y be two events such that P(X/Y) = \({1\over2},P(Y/X)={1\over3}\) and \(P(X\cap Y)={1\over6}\), then P(X\(\cup\)Y) is

(a)

\({1\over3}\)

(b)

\({2\over5}\)

(c)

\({1\over6}\)

(d)

\({2\over3}\)

If two events A and B are such that \(P(\overline{A})={3\over10}\) and \(P(A \cap \overline{B})={1\over2},\) then \(P(A\cap B)\) is

(a)

\({1\over2}\)

(b)

\({1\over3}\)

(c)

\({1\over4}\)

(d)

\({1\over5}\)

It is given that the events A and B are such that \(P(A)={1\over4},P(A/B)={1\over2}\) and \(P(B/A)={2\over3}.\) Then P(B) is

(a)

\({1\over 6}\)

(b)

\({1\over 3}\)

(c)

\({2\over 3}\)

(d)

\({1\over 2}\)

A coin is tossed three times. If events A and B are defined as A = Two heads occurs B = Last should be head. Then A and B are

(a)

Independent

(b)

dependent

(c)

both

(d)

mutually exclusive

If S is the sample space, P(A) = \(\frac { 1 }{ 3 } \)  P(B) and S = A\(\cup \)B, where A and B are mutually exclusive events then P(A) =

(a)

\(\frac { 1 }{ 4 } \)

(b)

\(\frac { 1 }{ 2 } \)

(c)

\(\frac { 3 }{ 4 } \)

(d)

\(\frac { 3 }{ 8 } \)

If A and B are two events such that P(A) = \(\frac { 4 }{ 5 } \) and \(P(A\cap B)=\frac { 7 }{ 10 } \) then P(B/A) = 

(a)

\(\frac { 1 }{ 10 } \)

(b)

\(\frac { 1 }{ 8 } \)

(c)

\(\frac { 7 }{ 8 } \)

(d)

\(\frac { 17 }{ 20 } \)

If P(B)=\(\frac { 3 }{ 5 } \)P(A/B) = \(\frac { 1 }{ 2 } \) and \(P(A\cup B)=\frac { 4 }{ 5 } \), then P(A) is

(a)

\(\frac { 3 }{ 10 } \)

(b)

\(\frac { 1 }{ 2 } \)

(c)

\(\frac { 1 }{ 10 } \)

(d)

\(\frac { 3 }{ 5 } \)