91Ó°ÊÓ

The probability that student A will fail a certain statistics examination is

\(P\left( A \right) = 0.5\)

The probability that student B will fail a certain statistics examination is:

\(P\left( B \right) = 0.2\)

The probability that both students A and B will fail the examination is:

\(P\left( {A \cap B} \right) = 0.1\)

The probability that neither student A nor student B will fail the examination is obtained as:

\(\) \(\begin{aligned}{}P{\left( {A \cup B} \right)^c} &= 1 - P\left( {A \cup B} \right)\\ &= 1 - \left( {P\left( A \right) + P\left( B \right) - P\left( {A \cap B} \right)} \right)\\ &= 1 - \left( {0.5 + 0.2 - 0.1} \right)\\ &= 1 - 0.6\\ = 0.4\end{aligned}\)

Thus the required probability is:\(P{\left( {A \cup B} \right)^c} = 0.4\)