A number is chosen from the first 100 natural | vedclass

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

Question

(D) Let $S$ be the set of the first $100$ natural numbers,so $n(S) = 100$.Let $A$ be the event that the number is even. The even numbers are $2, 4, 6,

Vedclass · Accepted Answer

$\frac{3}{5}$

Vedclass · Answer

(D) Let $S$ be the set of the first $100$ natural numbers,so $n(S) = 100$.Let $A$ be the event that the number is even. The even numbers are $2, 4, 6, \dots, 100$. Thus,$n(A) = 50$.Let $B$ be the event that the number is divisible by $5$. The numbers divisible by $5$ are $5, 10, 15, \dots, 100$. Thus,$n(B) = 20$.The intersection $A \cap B$ represents numbers that are both even and divisible by $5$,which means they are divisible by $10$. These are $10, 20, 30, \dots, 100$. Thus,$n(A \cap B) = 10$.Using the inclusion-exclusion principle,the number of favorable outcomes is $n(A \cup B) = n(A) + n(B) - n(A \cap B) = 50 + 20 - 10 = 60$.The probability is $P(A \cup B) = \frac{n(A \cup B)}{n(S)} = \frac{60}{100} = \frac{3}{5}$.

$A$ number is chosen from the first $100$ natural numbers. The probability that the number is even or divisible by $5$ is:

Similar Questions

$A$ coin is tossed $3$ times by $2$ persons. What is the probability that both get an equal number of heads?

Fifteen persons,including $A$ and $B$,sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$ is

Twenty tickets are marked with the numbers $1, 2, \dots, 20$. If three tickets are drawn at random,what is the probability that those marked $7$ and $11$ are among them?

In a single throw of two dice,the probability of obtaining a total of $7$ or $9$ is:

From a group of $7$ men and $4$ ladies,a committee of $6$ persons is formed. What is the probability that the committee contains exactly $2$ ladies?

Vedclass Test Series

Exam Paper Generator

Online Exam Module