Let A and B be two independent events of an e | vedclass

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

Question

(A) Given $P(A) = 0.3$ and $P(A \cup B) = 0.8$.Since $A$ and $B$ are independent,$P(A \cap B) = P(A)P(B)$.Using the addition theorem: $P(A \cup B) = P

Vedclass · Accepted Answer

$\frac{32}{35}$

Vedclass · Answer

(A) Given $P(A) = 0.3$ and $P(A \cup B) = 0.8$.Since $A$ and $B$ are independent,$P(A \cap B) = P(A)P(B)$.Using the addition theorem: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.$0.8 = 0.3 + P(B) - 0.3P(B)$.$0.5 = 0.7P(B) \Rightarrow P(B) = \frac{0.5}{0.7} = \frac{5}{7}$.The conditional statement $A 	o B$ is equivalent to $
eg A \lor B$,so $P(A 	o B) = P(
eg A \cup B) = 1 - P(A \cap 
eg B)$.Since $A$ and $B$ are independent,$A$ and $
eg B$ are also independent.$P(A \cap 
eg B) = P(A)P(
eg B) = 0.3 	imes (1 - \frac{5}{7}) = 0.3 	imes \frac{2}{7} = \frac{3}{10} 	imes \frac{2}{7} = \frac{6}{70} = \frac{3}{35}$.Therefore,$P(A 	o B) = 1 - \frac{3}{35} = \frac{32}{35}$.

Let $A$ and $B$ be two independent events of an experiment. If $P(A) = 0.3$ and $P(A \cup B) = 0.8$,then find $P(A \to B)$,where $P(X)$ denotes the probability that statement $X$ is true.

Similar Questions

If $P(A \cup B) = \frac{2}{3}$,$P(A \cap B) = \frac{1}{6}$,and $P(A) = \frac{1}{3}$,then which of the following is true?

$A$,$B$,and $C$ are three events,one of which must and only one can happen. The odds in favor of $A$ are $4 : 6$,and the odds against $B$ are $7 : 3$. Thus,the odds against $C$ are:

If $A$ and $B$ are mutually exclusive events,then the value of $P(A \cup B)$ is

The probabilities of occurrence of two events are respectively $0.21$ and $0.49$. The probability that both occur simultaneously is $0.16$. Then the probability that none of the two occurs is

Two dice are thrown simultaneously. The probability that the sum is odd or less than $7$ or both is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module