A die is thrown. Let A be event that number obtained is greater than 3. Let B be event that number o

English

Gujarati

Hindi

14.Probability

easy

A die is thrown. Let $A$ be the event that the number obtained is greater than $3.$ Let $B$ be the event that the number obtained is less than $5.$ Then $P\left( {A \cup B} \right)$ is

A

$\frac{3}{5}$

B

$0$

C

$1$

D

$\frac{2}{5}$

(AIEEE-2008)

Solution

$A=\{4 ; 5,6\}$ and $B=\{1,2,3,4\}$

$A \cap B=\{4\}$

[by addition theorem of probability] $P(A \cup B)=P(A)+P(B)-P(A \cap B)$

$P(A \cup B)=\frac{3}{6}+\frac{4}{6}-\frac{1}{6}=1$

Standard 11

Mathematics

Share

Similar Questions

Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happens is $\frac{1}{{12}}$ and the probability that neither $E$ nor $F$ happens is $\frac{1}{2},$ then

hard

(IIT-1993)

$A$ and $B$ are two independent events. The probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$. Then the probability of the two events are respectively

medium

The probability that a student will pass the final examination in both English and Hindi is $0.5$ and the probability of passing neither is $0.1$. If the probability of passing the English examination is $0.75$, what is the probability of passing the Hindi examination?

medium

If the odds against an event be $2 : 3$, then the probability of its occurrence is

easy

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 of both of them occur together is

hard

(JEE MAIN-2020)