Let A and B be two events such that P(overlin | vedclass

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

Question

(A) Given $P(\overline{A \cup B}) = \frac{1}{6}$ and $P(A \cap B) = \frac{1}{4}$.Since $P(\bar{A}) = \frac{1}{4}$,we have $P(A) = 1 - \frac{1}{4} = \f

Vedclass · Accepted Answer

Independent but not equally likely

Vedclass · Answer

(A) Given $P(\overline{A \cup B}) = \frac{1}{6}$ and $P(A \cap B) = \frac{1}{4}$.Since $P(\bar{A}) = \frac{1}{4}$,we have $P(A) = 1 - \frac{1}{4} = \frac{3}{4}$.We know that $P(\overline{A \cup B}) = 1 - P(A \cup B) = 1 - [P(A) + P(B) - P(A \cap B)]$.Substituting the values: $\frac{1}{6} = 1 - [\frac{3}{4} + P(B) - \frac{1}{4}] = 1 - [\frac{1}{2} + P(B)] = \frac{1}{2} - P(B)$.Thus,$P(B) = \frac{1}{2} - \frac{1}{6} = \frac{3-1}{6} = \frac{2}{6} = \frac{1}{3}$.Now,check for independence: $P(A) 	imes P(B) = \frac{3}{4} 	imes \frac{1}{3} = \frac{1}{4}$.Since $P(A \cap B) = P(A) 	imes P(B) = \frac{1}{4}$,the events $A$ and $B$ are independent.Since $P(A) = \frac{3}{4}$ and $P(B) = \frac{1}{3}$,$P(A) 
eq P(B)$,so they are not equally likely.Therefore,the events $A$ and $B$ are independent but not equally likely.

Let $A$ and $B$ be two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$,and $P(\bar{A}) = \frac{1}{4}$,where $\bar{A}$ stands for the complement of event $A$. Then events $A$ and $B$ are

Similar Questions

The chance of throwing a total of $7$ or $12$ with $2$ dice is:

$A$ bag contains $9$ discs of which $4$ are red,$3$ are blue and $2$ are yellow. The discs are similar in shape and size. $A$ disc is drawn at random from the bag. Calculate the probability that it will be red. (in $/9$)

$A$ bag contains $3$ white,$3$ black and $2$ red balls. Three balls are drawn one by one without replacement. The probability that the third ball is red is:

Two dice are thrown simultaneously. The probability of obtaining a total score of $5$ is

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$. Then,the probability that both of them occur together is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module