Question

If two events A and B are such that P(A') = 0.3, P(2) = 0.4 and P(A ∩ B') = 0.5, then P equals:

• A. ¾
• B. 5/6
• C. ¼
• D. 3/7

Answer 1

Answer: (C)

¼

Answer 2

P(A') = 0.3, P(2) = 0.4 and P(A ∩ B') = 0.5, P

$\left( \frac { B } { A \cap B ^ { \prime } } \right)$ = ?

$\mathrm { P } \left( \frac { \mathrm { B } } { \mathrm { A } \cap \mathrm { B } ^ { \prime } } \right) = \frac { \mathrm { P } \left( \mathrm { B } \cap \left( \mathrm { A } \cup \mathrm { B } ^ { \prime } \right) \right) } { \mathrm { P } \left( \mathrm { A } \cup \mathrm { B } ^ { \prime } \right) } = \frac { \mathrm { P } ( \mathrm { AB } ) } { 1 - \mathrm { P } \left( \mathrm { A } ^ { \prime } \mathrm { B } \right) }$

P(A ∩B') = P(1) - P(AB)

⇒ P(AB) = P(1) - P(A ∩ B')

= 0.7 - 0.5 = 0.2

P(A' ∩ B) = P(2) - P(AB)

= 0.4 - 0.2 = 0.2

So, $\mathrm { P } \left( \frac { \mathrm { B } } { \mathrm { A } \cup \mathrm { B } ^ { \prime } } \right) = \frac { 0.2 } { 1 - 0.2 } = \frac { 1 } { 4 }$.