If $A$ and $B$ are two events,what is the probability that exactly one of them occurs?
- A$P(A) + P(B) - P(A \cap B)$
- B$P(A) + P(B) - 2P(A \cap B)$
- C$P(A) + P(B) - P(A \cup B)$
- D$P(A) + P(B) - 2P(A \cup B)$
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Let $A$ and $B$ be events in a sample space $S$ such that $P(A)=0.5$, $P(B)=0.4$ and $P(A \cup B)=0.6$. Observe the following lists. Match List-$I$ with List-$II$ and select the correct option.
List-$I$ List-$II$ $(i) \ P(A \cap B)$ $(1) \ 0.4$ $(ii) \ P(A \cap \bar{B})$ $(2) \ 0.2$ $(iii) \ P(\bar{A} \cap B)$ $(3) \ 0.3$ $(iv) \ P(\bar{A} \cap \bar{B})$ $(4) \ 0.1$
| List-$I$ | List-$II$ |
| $(i) \ P(A \cap B)$ | $(1) \ 0.4$ |
| $(ii) \ P(A \cap \bar{B})$ | $(2) \ 0.2$ |
| $(iii) \ P(\bar{A} \cap B)$ | $(3) \ 0.3$ |
| $(iv) \ P(\bar{A} \cap \bar{B})$ | $(4) \ 0.1$ |
DifficultAP EAMCET 2011
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