Question

A number is chosen at random from the first 100 positive integers. Find the probability that the number is a multiple of 7. 7/50 3/20 13/100

Answer 1

$|\Omega|=100\\ |A|=14\\\\ P(A)=\dfrac{14}{100}=\dfrac{7}{50}$

Answer 2

Answer:

Option 1 - $\text{Probability}=\frac{7}{50}$

Step-by-step explanation:

Given : A number is chosen at random from the first 100 positive integers.

To Find : The probability that the number is a multiple of 7?

Solution :

The number of multiples of 7 in first 100 positive integers.

We apply arithmetic progression,

Where, a=7 is the first term

d=7 is the common difference

Last term is $a_n=98$

The formula of last term is

$a_n=a+(n-1)d$

$98=7+(n-1)7$

$98=7+7n-7$

$98=7n$

$n=\frac{98}{7}$

$n=14$

The number of term which is a multiple of 7 is 14.

favorable outcome = 14

Total number of outcome = 100

Probability that the number is a multiple of 7 is

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcome}}$

$\text{Probability}=\frac{14}{100}$

$\text{Probability}=\frac{7}{50}$

Therefore, Probability that the number is a multiple of 7 is $\frac{7}{50}$

So, Option 1 is correct.