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  •  Suppose and <img alt="\mathrm{B}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathr

 Suppose \mathrm{A} and \mathrm{B} are two independent events with probabilities \mathrm{P(A) \neq 0} and \mathrm{P(B) \neq 0}. Let \mathrm{\bar{A}} and \mathrm{\bar{B}} be their complements. Which one of the following statements is FALSE?

Option: 1

\mathrm{\quad P(A \cap B)=P(A) P(B)}


Option: 2

\mathrm{\quad P(A \mid B)=P(A)}


Option: 3

\mathrm{\quad P(A \cup B)=P(A)+P(B)}


Option: 4

\mathrm{P(\bar{A} \cap \bar{B})=P(\bar{A}) \cdot P(\bar{B})}


Answers (1)

best_answer

If \mathrm{A} and \mathrm{B} are independent events then

\mathrm{P(A \cap B) =P(A) P(B)}
\mathrm{P(A / B) =\frac{P(A \cap B)}{P(B)}=\frac{P(A) P(B)}{P(B)} }
\mathrm{=P(A)}
If \mathrm{A} and \mathrm{B} are independent events then \mathrm{P(\bar{A})} and \mathrm{P(\bar{B})} are also independent.
\mathrm{\&\quad P(A \cup B)=P(A)+P(B)-P(A \cap B)}

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manish painkra

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