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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 \(\leq \ldots \ldots.\).
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The correct answer is:
0.5
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.
\(\because\) 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.
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