Question

The probability of student A passing an examination is 2/9 and of student B passing is 5/9. Assuming the two events : 'A passes', 'B passes' as independent, find the probability of : (i) only A passing the examination (ii) only one of them passing the examination.

Answer 1

\[P\left( \text{ A passing examination }  \right) = \frac{2}{9}\]

\[P\left( \text{ B passing examination  } \right) = \frac{5}{9}\]

\[\left( i \right) P\left( \text{ only A passing examination}  \right) = P\left( \text{ A passes}  \right) P\left( B \text{ fails } \right)\]

\[ = \frac{2}{9}\left( 1 - \frac{5}{9} \right)\]

\[ = \frac{2}{9} \times \frac{4}{9}\]

\[ = \frac{8}{81}\]

\[\left( ii \right) P\left( \text{ only one of them passing examination } \right) = P\left( A\text{ passes and B fails }\right) + P\left( \text{ B passes and A fails }  \right)\]

\[ = \frac{2}{9} \times \left( 1 - \frac{5}{9} \right) + \frac{5}{9} \times \left( 1 - \frac{2}{9} \right)\]

\[ = \frac{8}{81} + \frac{35}{81}\]

\[ = \frac{43}{81}\]