Question

Alexio has 100 cards numbered 1-100, inclusive, and places them in a box. alexio then chooses a card from the box at random. what is the probability that the number on the card he chooses is a multiple of 2, 3 or 5? express your answer as a common fraction

Answer 1

We are given

Alexio has 100 cards numbered 1-100, inclusive, and places them in a box

so, total number of outcomes =100

now, we have chooses a card from the box at random

that is multiple of 2 , 3 or 5

so, firstly, we will find number of possible outcomes that is multiple of 2 , 3 or 5

Firstly, we will find which can't be multiple of 2, 3 and 5

that will be

={ 1, 7,11,13,17,19 , 23 , 29 , 31 , 37 , 41, 43 , 47 , 49 , 53, 59 , 61 , 67, 71, 77, 79, 83, 89 , 91 , 97 }

so,

number of possible outcomes =100-25=75

now, we can find probability

probability = (number of possible outcomes )/(total number of outcomes)

now, we can plug values

and we get

$p=\frac{75}{100}$

$p=\frac{3}{4}$.................Answer