If the probability for \(A\) to fail in an exam is 0.2 and that for \(B\) is 0.3, then the probability that…
If the probability for \(A\) to fail in an exam is 0.2 and that for \(B\) is 0.3, then the probability that either \(A\) or \(B\) fails is \(\leq \ldots \ldots.\).
0.2
0.4
0.5
0.3
Solution
Let, \(P(A)\) is the probability for \(A\) to fail in an exam and \(P(B)\) is the probability for \(B\) to fail in an exam.
\(\because\) The probability that either \(A\) or \(B\) fails is
\(\begin{array}{cc}
& P(A \cup B)=P(A)+P(B)-P(A \cap B) \\
& \Rightarrow P(A \cup B) \leq P(A)+P(B) \\
& \Rightarrow P(A \cup B) \leq 0.2+0.3 \\
& \quad\{\because P(A)=0.2 \text { and } P(B)=0.3 \text { given}\} \\
& \Rightarrow P(A \cup B) \leq 0.5
\end{array}\)
Hence, option (c) is correct.