Probability Question 157
Question: If $ A_1,A_2,…A_{n} $ are any n events, then
Options:
A) $ P(A_1\cup A_2\cup …\cup A_{n})=P(A_1)+P(A_2)+…+P(A_{n}) $
B) $ P(A_1\cup A_2\cup …\cup A_{n})>P(A_1)+P(A_2)+…+P(A_{n}) $
C) $ P(A_1\cup A_2\cup …\cup A_{n})\le P(A_1)+P(A_2)+…+P(A_{n}) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
For any two events $ A $ and $ B, $ we have
$ P(A\cup B)=P(A)+P(B)-P(A\cap B) $
$ \therefore P(A\cup B)\le P(A)+P(B). $
Using principle of mathematical induction, it can be easily established that
$ P( \underset{i=1}{\overset{n}{\mathop{\cup }}}A_{i} )\le \sum\limits_{i=1}^{n}{P(A_{i}).} $
BETA
