(B) We know that $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Since $P(A) = 1 - P(A^C) = 1 - \frac{1}{2} = \frac{1}{2}$.Substituting the values into the

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

(B) We know that $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Since $P(A) = 1 - P(A^C) = 1 - \frac{1}{2} = \frac{1}{2}$.Substituting the values into the addition theorem of probability:$\frac{5}{6} = \frac{1}{2} + P(B) - \frac{1}{3}$.$\frac{5}{6} = \frac{3-2}{6} + P(B) = \frac{1}{6} + P(B)$.$P(B) = \frac{5}{6} - \frac{1}{6} = \frac{4}{6} = \frac{2}{3}$.Therefore,$P(B^C) = 1 - P(B) = 1 - \frac{2}{3} = \frac{1}{3}$.

Class 11 Mathematics Probability Odds in favor and odds against, Addition theorem on probability

Easy

If $A$ and $B$ are two events with $P(A \cap B) = \frac{1}{3}$,$P(A \cup B) = \frac{5}{6}$,and $P(A^C) = \frac{1}{2}$,then the value of $P(B^C)$ is

AP EAMCET 2021 All AP EAMCET

A
$\frac{1}{2}$
B
$\frac{1}{3}$
C
$\frac{2}{3}$
D
$\frac{5}{6}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Probability

Subtopic

Odds in favor and odds against, Addition theorem on probability

Previous Year

AP EAMCET 2021 Paper All AP EAMCET years →

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

Medium

View Solution

If $E$ and $F$ are events such that $P(E)=\frac{1}{4}$,$P(F)=\frac{1}{2}$ and $P(E \cap F)=\frac{1}{8}$,find $P(\text{not } E \text{ and not } F)$.

Easy

View Solution

$A$ doctor schedules an appointment for a patient in the month of November. What is the probability that the date is a multiple of $5$ or $6$?

Easy

View Solution

An event has odds in favour $4 : 5$. Then,the probability that the event occurs is:

Easy

View Solution

The probability of an event happening is the square of the probability of a second event,but the odds against the first are the cube of the odds against the second. The probabilities of the events are:

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $A$ and $B$ are two events with $P(A \cap B) = \frac{1}{3}$,$P(A \cup B) = \frac{5}{6}$,and $P(A^C) = \frac{1}{2}$,then the value of $P(B^C)$ is

Similar Questions

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

If $E$ and $F$ are events such that $P(E)=\frac{1}{4}$,$P(F)=\frac{1}{2}$ and $P(E \cap F)=\frac{1}{8}$,find $P(\text{not } E \text{ and not } F)$.

$A$ doctor schedules an appointment for a patient in the month of November. What is the probability that the date is a multiple of $5$ or $6$?

An event has odds in favour $4 : 5$. Then,the probability that the event occurs is:

The probability of an event happening is the square of the probability of a second event,but the odds against the first are the cube of the odds against the second. The probabilities of the events are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module