For two events A and B,a true statement among | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We know that by the definition of conditional probability: $P(\frac{B}{A}) = \frac{P(A \cap B)}{P(A)}$ $\Rightarrow P(A) P(\frac{B}{A}) = P(A \cap

Vedclass · Accepted Answer

$P(\bar{A} \cup \bar{B}) = 1 - P(A) P(\frac{B}{A})$

Vedclass · Answer

(A) We know that by the definition of conditional probability: $P(\frac{B}{A}) = \frac{P(A \cap B)}{P(A)}$ $\Rightarrow P(A) P(\frac{B}{A}) = P(A \cap B)$ Now,using De Morgan's Law,we have: $P(\bar{A} \cup \bar{B}) = P(\overline{A \cap B})$ Using the property of complement events,$P(\bar{E}) = 1 - P(E)$: $P(\overline{A \cap B}) = 1 - P(A \cap B)$ Substituting the value of $P(A \cap B)$ from the first step: $P(\bar{A} \cup \bar{B}) = 1 - P(A) P(\frac{B}{A})$ Thus,option $A$ is the correct statement.

For two events $A$ and $B$,a true statement among the following is

Similar Questions

$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B | A)$ if $A \cap B = \phi$.

If $A$ and $B$ are events,such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$,then $P(B)$ is

Events $A$ and $B$ are such that $P(A)=\frac{1}{2}$,$P(B)=\frac{7}{12}$ and $P(\text{not } A \text{ or not } B)=\frac{1}{4}$. State whether $A$ and $B$ are independent?

For two events $A$ and $B$,if $P(A) = P(A|B) = \frac{1}{4}$ and $P(B|A) = \frac{1}{2}$,then:

Let $A$ and $B$ be two events such that $P(B \mid A) = \frac{2}{5}$,$P(A \mid B) = \frac{1}{7}$ and $P(A \cap B) = \frac{1}{9}$. Consider:
$(S1) P(A' \cup B) = \frac{5}{6}$
$(S2) P(A' \cap B') = \frac{1}{18}$.
Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module