(D) Given that $A \subset B$,we have $A \cap B = A$.The conditional probability is defined as $P(A|B) = \frac{P(A \cap B)}{P(B)}$.Substituting $A \cap

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(D) Given that $A \subset B$,we have $A \cap B = A$.The conditional probability is defined as $P(A|B) = \frac{P(A \cap B)}{P(B)}$.Substituting $A \cap B = A$,we get $P(A|B) = \frac{P(A)}{P(B)}$.Since $A \subset B$,it follows that $P(B) \le 1$.Therefore,$\frac{1}{P(B)} \ge 1$.Multiplying both sides by $P(A)$,we get $\frac{P(A)}{P(B)} \ge P(A)$.Thus,$P(A|B) \ge P(A)$.

Class 12 Mathematics Probability Conditional probability

Difficult

Let $A$ and $B$ be two non-null events such that $A \subset B$. Then,which of the following statements is always correct?

JEE MAIN 2019 All JEE MAIN

A
$P(A|B) = 1$
B
$P(A|B) \le P(A)$
C
$P(A|B) = P(B) - P(A)$
D
$P(A|B) \ge P(A)$

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Probability

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Conditional probability

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JEE MAIN 2019 Paper All JEE MAIN years →

Find $P(E | F)$ for a coin tossed three times,where $E: \text{head on third toss}$,$F: \text{heads on first two tosses}$.

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If two events $A$ and $B$ are such that $P(\overline{A}) = 0.3$,$P(B) = 0.4$,and $P(A \cap \overline{B}) = 0.5$,then $P(B | (A \cup \overline{B})) = $

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MediumAIEEE 2008

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If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$,then which of the following is correct?

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Let $A$ and $B$ be two non-null events such that $A \subset B$. Then,which of the following statements is always correct?

Similar Questions

Find $P(E | F)$ for a coin tossed three times,where $E: \text{head on third toss}$,$F: \text{heads on first two tosses}$.

Given that $E$ and $F$ are events such that $P(E)=0.6$,$P(F)=0.3$,and $P(E \cap F)=0.2$,find $P(E|F)$ and $P(F|E)$.

If two events $A$ and $B$ are such that $P(\overline{A}) = 0.3$,$P(B) = 0.4$,and $P(A \cap \overline{B}) = 0.5$,then $P(B | (A \cup \overline{B})) = $

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