Question

The probability that a particular day in the month of july is a

rainy day is $\frac { 3 } { 4 }$ . Two person whose credibility are $\frac { 4 } { 5 }$ and $\frac { 2 } { 3 }$

respectively claim that 15^th july was a rainy day. The probability that it was real a rainy day.

• A. $\frac { 3 } { 4 }$
• B. $\frac { 24 } { 25 }$
• C. $\frac { 8 } { 9 }$
• D. None of these

Answer 1

Answer: (B)

$\frac { 24 } { 25 }$

Answer 2

A : Event that first man speaks truth

B : Event that second man speaks truth

R : Day is rainy

P(R)= $\frac { \mathrm { P } ( \mathrm { A } \cap \mathrm { B } ) \cdot \mathrm { P } ( \mathrm { R } ) } { \mathrm { P } ( \mathrm { A } \cap \mathrm { B } ) \cdot \mathrm { P } ( \mathrm { R } ) + \mathrm { P } ^ { \prime } \left( \mathrm { A } ^ { \prime } \cap \mathrm { B } ^ { \prime } \right) \cdot \mathrm { P } \left( \mathrm { R } ^ { \prime } \right) }$ =$\frac { \frac { 4 } { 5 } \cdot \frac { 2 } { 3 } \cdot \frac { 3 } { 4 } } { \frac { 4 } { 5 } \cdot \frac { 2 } { 3 } \cdot \frac { 3 } { 4 } + \frac { 1 } { 5 } \cdot \frac { 1 } { 3 } \cdot \frac { 1 } { 4 } }$

= $\frac { 24 } { 25 }$