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A, B are two events and $\bar{A}$ denotes the complements of A. Consider the following statements
$1 \quad P(A \cup B) \leq P(B)+P(A)$
$2 \quad \mathrm{P}(\mathrm{A})+\mathrm{P}(\overline{\mathrm{A}} \cup \mathrm{B}) \leq 1+\mathrm{P}(\mathrm{B})$
Which of the above statements is/are correct?
Options:
$1 \quad P(A \cup B) \leq P(B)+P(A)$
$2 \quad \mathrm{P}(\mathrm{A})+\mathrm{P}(\overline{\mathrm{A}} \cup \mathrm{B}) \leq 1+\mathrm{P}(\mathrm{B})$
Which of the above statements is/are correct?
Solution:
1846 Upvotes
Verified Answer
The correct answer is:
Both 1 and 2
(1) $\mathrm{P}(\mathrm{A} \cup \mathrm{B}) \leq \mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})$ is correct
and (2) $\mathrm{P}(\mathrm{A})+\mathrm{P}(\overline{\mathrm{A}} \cup \mathrm{B}) \leq 1+\mathrm{P}(\mathrm{B})$ is also correct
$\Rightarrow$ Both the given statement are correct.
and (2) $\mathrm{P}(\mathrm{A})+\mathrm{P}(\overline{\mathrm{A}} \cup \mathrm{B}) \leq 1+\mathrm{P}(\mathrm{B})$ is also correct
$\Rightarrow$ Both the given statement are correct.
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