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)=(14)/(100)=(7)/(50)`

Answer 2

Option 1 -
`\text{Probability}=(7)/(50)`

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=(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}=(14)/(100)`

`\text{Probability}=(7)/(50)`

Therefore, Probability that the number is a multiple of 7 is
`(7)/(50)`

So, Option 1 is correct.