If A and B are any two events such that P(A) | vedclass

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

Question

(A) Given the equation $P(A) + P(B) - P(A \cap B) = P(A)$.
Subtracting $P(A)$ from both sides, we get $P(B) - P(A \cap B) = 0$, which implies $P(B) =

Vedclass · Accepted Answer

$P(A|B) = 1$

Vedclass · Answer

(A) Given the equation $P(A) + P(B) - P(A \cap B) = P(A)$.
Subtracting $P(A)$ from both sides, we get $P(B) - P(A \cap B) = 0$, which implies $P(B) = P(A \cap B)$.
This equality indicates that $B \subseteq A$, meaning all outcomes of event $B$ are contained within event $A$.
By the definition of conditional probability, $P(A|B) = \frac{P(A \cap B)}{P(B)}$.
Since $P(A \cap B) = P(B)$, we substitute this into the formula:
$P(A|B) = \frac{P(B)}{P(B)} = 1$ (assuming $P(B) 
eq 0$).

If $A$ and $B$ are any two events such that $P(A) + P(B) - P(A \cap B) = P(A)$, then $\dots \dots \dots$

Similar Questions

$A$ die is thrown three times and the sum of the numbers obtained is $15$. What is the probability that the number $4$ appears in the first throw?

Two numbers are selected at random from the set $\{1, 2, 3, \ldots, 13\}$. If the sum of the selected numbers is even, what is the probability that both the numbers are odd?

When $2$ dice are thrown, it is observed that the sum of the numbers appearing on the top faces of both dice is a prime number. What is the probability that at least one of the numbers in the pair is a multiple of $3$?

If two dice are rolled, then the probability of getting a multiple of $3$ as the sum of the numbers appeared on the top faces of the dice, given that their sum is an odd number, is

$A$ family has two children. What is the probability that both the children are boys given that at least one of them is a boy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module