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 can be expressed as $k^3

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 can be expressed as $k^3$ 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

$A$ natural number is selected at random from the set $\{x \in \mathbb{N} : 1 \leq x \leq 100\}$. The probability that the number satisfies the inequation $x^2 - 13x \leq 30$ is:

What is the probability of having $53$ Sundays in a non-leap year?

Suppose $3$ bulbs are selected at random from a lot. Each bulb is tested and classified as defective $(D)$ or non-defective $(N)$. Write the sample space of this experiment.

If two subsets $A$ and $B$ are selected at random from a set $S$ containing $n$ elements,then the probability that $A \cap B = \phi$ and $A \cup B = S$ is

When a fair die is rolled once,what is the probability of getting $1$ or $6$ on the top face?

Vedclass Test Series

Exam Paper Generator

Online Exam Module