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

The probability that the number on the card Alexio chooses is a multiple of 2, 3, or 5 is 37/50.

Step-by-step explanation:

To find the probability that the number on the card Alexio chooses is a multiple of 2, 3, or 5, we need to find the total number of cards that are multiples of 2, 3, or 5 and divide it by the total number of cards.

There are 50 cards that are multiples of 2 (2, 4, 6, ..., 100), 33 cards that are multiples of 3 (3, 6, 9, ..., 99), and 20 cards that are multiples of 5 (5, 10, 15, ..., 100). However, some cards are multiples of two of these numbers, so we need to adjust for double counting.

The cards that are multiples of both 2 and 3 (6, 12, 18, ..., 96) are counted twice, so we subtract them once. Similarly, the cards that are multiples of both 2 and 5 (10, 20, 30, ..., 100) and the cards that are multiples of both 3 and 5 (15, 30, 45, ..., 90) are each counted twice and need to be subtracted once.

Therefore, the total number of cards that are multiples of 2, 3, or 5 is 50 + 33 + 20 - 16 - 10 - 6 + 3 = 74.

There are 100 cards in total, so the probability that Alexio chooses a card that is a multiple of 2, 3, or 5 is 74/100 = 37/50.

Answer 2

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=(75)/(100)`

`p=(3)/(4)`.................Answer