A) \[\frac{1}{7}\]
B) \[\frac{4}{7}\]
C) \[\frac{2}{7}\]
D) \[\frac{5}{7}\]
E) \[\frac{6}{7}\]
Correct Answer: C
Solution :
We have\[p(B)=\frac{1}{3},p(A\cup B)=\frac{13}{21}\] For mutually exclusive events A and B, we get \[p(A\cup B)=p(A)+p(B)\] \[\Rightarrow \] \[p(A)=p(A\cup B)-p(B)\] \[=\frac{13}{21}-\frac{1}{3}\] \[=\frac{13-7}{21}=\frac{6}{21}=\frac{2}{7}\] \[\therefore \] \[p(A)=\frac{2}{7}\]
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