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

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

Question

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

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(C) Given that $P(A \cup B) = \frac{5}{6}$,$P(A \cap B) = \frac{1}{3}$,and $P(\bar{B}) = \frac{1}{3}$.Since $P(B) = 1 - P(\bar{B})$,we have $P(B) = 1 - \frac{1}{3} = \frac{2}{3}$.Using the addition theorem of probability: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the values: $\frac{5}{6} = P(A) + \frac{2}{3} - \frac{1}{3}$.$\frac{5}{6} = P(A) + \frac{1}{3}$.$P(A) = \frac{5}{6} - \frac{1}{3} = \frac{5-2}{6} = \frac{3}{6} = \frac{1}{2}$.

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

Similar Questions

$A$ card is drawn at random from a pack of $52$ cards. The probability of this card being a red card or a queen is:

Three ships $A, B$ and $C$ sail from England to India. If the ratio of their arriving safely are $2 : 5, 3 : 7$ and $6 : 11$ respectively,then the probability of all the ships arriving safely is:

If ${A_1}, {A_2}, ..., {A_n}$ are any $n$ events,then:

One card is drawn from a pack of $52$ cards. The probability that it is a king or a diamond is

Three critics review a book. For the three critics,the odds in favour of the book are $2:5$,$3:4$,and $4:3$ respectively. The probability that the majority is in favour of the book is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module