Question

A positive integer is selected at random and is divided by 7,what is the probability that the remainder is 1?
a. 3/7
b. 4/7
c. 1/7
d. 2/7

Answer 1

a positive integer is selected at random and is divided by 7 7 that the remainder is 1/7

Answer 2

Answer:

Option c - $\frac{1}{7}$

Step-by-step explanation:

Given : A positive integer is selected at random and is divided by 7.

To find : What is the probability that the remainder is 1?

Solution :

The positive integer selected at random, will only be divisible by 7 giving remainder 1,

If it is in the form of (7n+1), where n is a natural number.

Then, The numbers, divisible by 7 giving remainder 1.

$7\times1+1 = 8\\7\times2+1 = 15\\7\times3+1=22\\7\times4+1=29$

ie, {8,9,10,11,12,13,14,} , {15,16,17,18,19,20,21}, {22,23,24,25,26,27,28}, {29,30,31,32,33,34,35,}, …………… & so on…

We have seen that there is only one such number, which when divided by 7, gives remainder 1.

So, Favorable outcome is 1.

Total outcome is 7.

Probability is given by,

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

$\text{Probability}=\frac{1}{7}$

Therefore, Option c is correct.