Question

a bag contains cards numbered 1 to 20 a card is drawn at random from the bag find probability that the number on the card is divisible by both 2 and 3

Answer 1

Total number of cards = 20

•p(a number divisible by 2) =10/20

•p( a number divisible by 3) =6/20

Answer 2

Given:

Cards numbered 1 to 20

To find:

The probability that the number on the card drawn is divisible by both 2 and 3

Solution:

The probability that the number on the card drawn is divisible by both 2 and 3 is 3/20.

We can find the probability by following the given steps-

We know that the probability can be obtained by dividing the favourable outcomes by the total possible outcomes of an event.

We are given that the cards have numbers from 1 to 20.

For a number to be divisible by both 2 and 3, it has to be divisible by the LCM of 2 ad 3.

The LCM of 2 and 3 is 6.

So, the favourable outcomes=Numbers between 1 and 20 that are divisible by 6

Numbers between 1 and 20 that are divisible by 6= 6, 12, 18

So, the number of cards divisible by both 2 and 3=3

The total number of cards=20

The probability that the number on the card drawn is divisible by both 2 and 3=Numbers on cards between 1 and 20 that are divisible by 6/ Total number of cards

On putting the values,

The probability that the number on the card drawn is divisible by both 2 and 3=3/20

Therefore, the probability that the number on the card drawn is divisible by both 2 and 3 is 3/20.