The probability that a number selected at ran | vedclass

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

Question

(A) The total number of elements in the set $S = \{1, 2, 3, \ldots, 100\}$ is $n(S) = 100$.$A$ number is a perfect cube if it is of the form $k^3$ for

Vedclass · Accepted Answer

$\frac{1}{25}$

Vedclass · Answer

(A) The total number of elements in the set $S = \{1, 2, 3, \ldots, 100\}$ is $n(S) = 100$.$A$ number is a perfect cube if it is of the form $k^3$ for some integer $k$.The perfect cubes in the given set are $1^3 = 1$, $2^3 = 8$, $3^3 = 27$, and $4^3 = 64$. Note that $5^3 = 125$, which is greater than $100$.Thus, the set of favorable outcomes is $A = \{1, 8, 27, 64\}$.The number of favorable outcomes is $n(A) = 4$.The required probability is $P(A) = \frac{n(A)}{n(S)} = \frac{4}{100} = \frac{1}{25}$.

The probability that a number selected at random from the set of numbers ${1, 2, 3, \ldots, 100}$ is a cube, is

Similar Questions

The energy required to accelerate a car from $10 \, m/s$ to $20 \, m/s$ is how many times the energy required to accelerate the car from rest to $10 \, m/s$?

The $IUPAC$ name for the complex $[Co(NO_2)(NH_3)_5]Cl_2$ is:

Which of the following reagents are required to prepare $3$-ethylpentan-$3$-ol?

Which of the following glands is responsible for immunity in humans?

The heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1 : 2$ and their lengths are in the ratio $2 : 1$. If the temperature difference between their ends is the same,the ratio of the rates of flow of heat through them will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module