Question

If two events A and B are such that P(A^C) = 0.3, P(2) = 0.4

and P(AB^C) = 0.5 then P[B/(A Č B^C)] is equal to-

• A. $\frac { 1 } { 4 }$
• B. $\frac { 1 } { 2 }$
• C. $\frac { 3 } { 4 }$
• D. $\frac { 2 } { 3 }$

Answer 1

Answer: (A)

$\frac { 1 } { 4 }$

Answer 2

P(A^C) = 0.3 Ž P(1) = 0.7

P(2) = 0.4 Ž P(B^C) = 0.6

P(AB^C) = 0.5 Ž P(1) –P (AB) = 0.5

or, P(AB) = 0.7 – 0.5 = 0.2

P [B/(A Ē B^C)] = $\frac { \mathrm { P } \left[ \mathrm { B } \cap \left( \mathrm { A } \cup \mathrm { B } ^ { \mathrm { C } } \right) \right] } { \mathrm { P } \left( \mathrm { A } \cup \mathrm { B } ^ { \mathrm { C } } \right) }$ …(1)

Now, B Ē (A Č B^C) = A Ē B

\ P [B Ē (A Č B^C)] = P(A Ē B) = 0.2 …(2)

and P (A Č B^C) = P (1) + P(B^C) –P (A Ē B^C)

= 0.7 + 0.6 – 0.5 = 0.8 …(3)

From (1), (2) and (3)

Required probability = $\frac { 1 } { 4 }$