Statistics And Probability Question 574
Question: In two events $ P(A\cup B)=5/6 $ , $ P(A^{c})=5/6 $ , $ P(B)=2/3, $ then A and B are
[UPSEAT 2001]
Options:
A) Independent
B) Mutually exclusive
C) Mutually exhaustive
D) Dependent
Show Answer
Answer:
Correct Answer: B
Solution:
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$ P(A{{}^{c}})=1-P(A) $
$ \Rightarrow $ $ P(A)=\frac{1}{6} $ Now $ P(A\cup B)=P(A)+P(B)-P(A\cap B) $
Þ $ \frac{5}{6}=\frac{1}{6}+\frac{2}{3}-P(A\cap B) $
Þ $ P(A\cap B)=0 $ Hence, events A and B are mutually exclusive.
BETA
