Question

A candidate has to attend Maths and Physics exams. The probability that he passes any exam is $\frac { 1 } { 4 }$ . Then the probability that he passes exactly one exam is

• A. 1/8
• B. 7/8
• C. 5/8
• D. 3/8

Answer 1

Answer: (D)

3/8

Answer 2

From the above problem,

$\mathrm { P } ( \mathrm { A } \cap \overline { \mathrm { B } } ) + \mathrm { P } ( \overline { \mathrm { A } } \cap \mathrm { B } ) = \mathrm { P } ( \mathrm { A } ) + \mathrm { P } ( \mathrm { B } ) - 2 \mathrm { P } ( \mathrm { A } \cap \mathrm { B } )$ = 3/8

$\mathrm { P } ( \mathrm { A } \cap \overline { \mathrm { B } } )$ + $\mathrm { P } ( \overline { \mathrm { A } } \cap \mathrm { B } )$ = P(1) $\mathrm { P } ( \overline { \mathrm { B } } ) + \mathrm { P } ( \overline { \mathrm { A } } )$ P(2)

= $\frac { 1 } { 4 } \times \frac { 3 } { 4 } + \frac { 1 } { 4 } \times \frac { 3 } { 4 } = \frac { 3 } { 8 }$ .