MCQ
If A and B are mutually exclusive events then:
- A$\text{P(A)}\leq\text{P}(\overline{\text{B}})$
- B$\text{P(A)}\geq\text{P}(\overline{\text{B}})$
- C$\text{P(A)}<\text{P}(\overline{\text{B}})$
- DNone of these
If A and B are mutually exclusive events then:
It is given that A and B are mutually exclusive events.
We know that,
$\text{P}(\text{A}\cup\text{B})=\text{P}(\text{A)}+\text{(B})-\text{P}(\text{A}\cap\text{B})$$\big[\text{From(1)}\big]$
$\Rightarrow\text{P}(\text{A}\cup\text{B})=\text{P}(\text{A)}+\text{P}\text{(B})$ $\big[\text{P}(\text{A}\cup\text{B})\leq1\big]$
$\Rightarrow\text{P}(\text{A)}+\text{P}\text{(B})\leq1$
$\Rightarrow\text{P}(\text{A)}\leq1-\text{P}\text{(B})=\text{P}(\overline{\text{B}})$
$\therefore\text{P}(\text{A)}\leq\text{P}\text{(B})$
Hence, the correct answer is option (a).$\therefore\text{P}(\text{A }\cap\text{B})=0\ ...(1)$
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The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then $\text{P}(\bar{\text{A}})+\text{P}(\bar{\text{B}})$ is:
Which of the following is the conditional p → q?