Question

A number between 1 and 10 is chosen at random . What is the probability of getting a multiple of 5 or an even number?

Answer 1

I have done 2 cases assuming question says number is chosen between 1 and 10 and number is chosen from 1 to 10.

Case 1:

Question says number between 1 and 10 is chosen at random

Sample set = {2,3,4,5,6,7,8,9} ----> Totally 8 numbers are present.

Multiple of 5 between 1 and 10 = {5} ----> 1 number present

Probabiltiy of multiple of 5 between 1 and 10 = 1/10

Even numbers present between 1 and 10 = {2,4,6,8} ------> 4 numbers present

Probability of getting an even number = 4/10 = 2/5

Numbers that are multiple of 5 and even numbers between 1 and 10 = { } -----> 0 number present

Probability of getting a mutliple of 5 and even number between 1 and 10 = 0/10 = 0

Probability of getting a multiple of 5 or even number between 1 and 10 = Probabiltiy of getting multiple of 5 + Probability of getting an even number - Probability of getting a mutliple of 5 and even number

= 1/10 + 2/5 - 0 = 1/2 or 0.5

So answer : 1/2 or 0.5

Case 2:

Assuming question says number from 1 to 10 is chosen at random

Sample set = {1,2,3,4,5,6,7,8,9,10} ----> Totally 10 numbers are present.

Multiple of 5 from 1 to 10 = {5,10} ----> 2 numbers present

Probabiltiy of getting multiple of 5 from 1 to 10 = 2/10 = 1/5

Even numbers present from 1 to 10 = {2,4,6,8,10} ------> 5 numbers present

Probability of getting an even number = 5/10 = 1/2

Numbers that are multiple of 5 and even numbers from 1 to 10 = {10} -----> 1 number present

Probability of getting a mutliple of 5 and even number = 1/10

Probability of getting a multiple of 5 or even number from 1 to 10 = Probabiltiy of getting multiple of 5 + Probability of getting an even number - Probability of getting a mutliple of 5 and even number

= 1/5 + 1/2 - 1/10 = 3/5 or 0.6

So answer : 3/5 or 0.6