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

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

Question

(A) Given $P(A \cup B) = \frac{5}{6}$,$P(A \cap B) = \frac{1}{3}$,and $P(\bar{A}) = \frac{1}{2}$.Since $P(A) = 1 - P(\bar{A}) = 1 - \frac{1}{2} = \fra

Vedclass · Accepted Answer

Independent

Vedclass · Answer

(A) Given $P(A \cup B) = \frac{5}{6}$,$P(A \cap B) = \frac{1}{3}$,and $P(\bar{A}) = \frac{1}{2}$.Since $P(A) = 1 - P(\bar{A}) = 1 - \frac{1}{2} = \frac{1}{2}$.Using the addition theorem: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.$\frac{5}{6} = \frac{1}{2} + P(B) - \frac{1}{3}$.$\frac{5}{6} = \frac{1}{6} + P(B) \Rightarrow P(B) = \frac{4}{6} = \frac{2}{3}$.Now,check for independence: $P(A) 	imes P(B) = \frac{1}{2} 	imes \frac{2}{3} = \frac{1}{3}$.Since $P(A \cap B) = P(A) 	imes P(B) = \frac{1}{3}$,the events $A$ and $B$ are independent.

If two events $A$ and $B$ are such that $P(A \cup B) = \frac{5}{6}$,$P(A \cap B) = \frac{1}{3}$,and $P(\bar{A}) = \frac{1}{2}$,then the events $A$ and $B$ are:

Similar Questions

The probability of at least one of the events $A$ and $B$ occurring is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.2$, then $P(\overline{A}) + P(\overline{B})$ is

If $A$ and $B$ are mutually exclusive events with $P(A)=\frac{1}{4}$ and $P(B)=\frac{3}{7}$,then what is the value of $P(A / A \cup B)$?

If a leap year is selected at random,what is the chance that it will contain $53$ Tuesdays?

$A$ card is drawn at random from a well-shuffled pack of $52$ cards. The probability that it is a black card or a face card is

When a pair of dice is thrown,what is the probability of getting an even number on each die?

Vedclass Test Series

Exam Paper Generator

Online Exam Module