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 $5$,i.e.,divisible by $10$. These are $10, 20, 30, \dots, 100$. Thus,$n(A \cap B) = 10$.Using the formula for the union of two sets: $n(A \cup B) = n(A) + n(B) - n(A \cap B) = 50 + 20 - 10 = 60$.The required 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

The number of $3$-digit numbers that are divisible by either $3$ or $4$ but not divisible by $48$ is:

The probability of choosing at random a number that is divisible by $6$ or $8$ from among $1$ to $90$ is equal to

Let $A = \{1, 6, 11, 16, \dots\}$ and $B = \{9, 16, 23, 30, \dots\}$ be the sets consisting of the first $2025$ terms of two arithmetic progressions. Then $n(A \cup B)$ is

If $A$ and $B$ are subsets of universal set $X$ such that $n(X)=200, n(A)=90, n(B)=80$ and $n(A' \cap B')=40$,then $n(A \cap B')=$

Let $S$ be the set of all triangles in the $xy$-plane,each having one vertex at the origin and the other two vertices lying on the coordinate axes with integral coordinates. If each triangle in $S$ has an area of $50$ sq. units,then the number of elements in the set $S$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module