KCET · Maths · Probability
The probability of happening of an event \( A \) is \( 0.5 \) and that of \( B \) is \( 0.3 \). If \( A \) and \( B \) are mutually
exclusiveevents, then the probability of neither A nor B is
- A \( 0.4 \)
- B \( 0.5 \)
- C \( 0.2 \)
- D \( 0.9 \)
Answer & Solution
Correct Answer
(C) \( 0.2 \)
Step-by-step Solution
Detailed explanation
\(P(A)=0.5\)
\(P(B)=0.3\)
\(P(A \cap B)=0\)
\(P(A \cup B)=P(A)+P(B)-P(A \cap B)\)
\(=0.5+0.3-0=0.8\)
\(\Rightarrow P(A \cup B)=1-P(A \cup B)\)
\(=1-0.8=0.2\)
\(P(B)=0.3\)
\(P(A \cap B)=0\)
\(P(A \cup B)=P(A)+P(B)-P(A \cap B)\)
\(=0.5+0.3-0=0.8\)
\(\Rightarrow P(A \cup B)=1-P(A \cup B)\)
\(=1-0.8=0.2\)
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