Question

From a set of 100 cards numbered 1 to 100, one card is drawn at random. find the probability that the number on the card is divisible by 6 or 8, but not by 24.

Answer 1

Hey !!

Answer:

$= \frac{1}{5}$

Step-by-step explanation:

Number divisible by 6 from 1 to 100 = 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 , 60 , 66 , 72 , 78 , 84 , 90 , 96

Number divisible by 8 from 1 to 100 = 8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72 , 80 , 88 , 96

∴ Number divisible by 6 or 8 but not by 24  from 1 to 100 = 6 , 8 , 12 , 16 , 18 , 30 , 32 , 36 , 40 , 42 , 54 , 56 , 60 , 64 , 66 , 78 , 84 , 88 , 90.

∴ Required probability = $\frac{20}{100}$

        = $\frac{1}{5}$

Good luck !!

Answer 2

The probability of drawing a card divisible by 6 and 8 but not 24 is 1:5.

Step-by-step explanation:

Given:

Total cards= 100

To find= the probability of drawing a card divisible by 6 and 8 but not 24

Solution:

The LCM of 6 and 8= 3×2×2×2

=24

So the numbers which are divisible by6 and 8 will also be divisible by 24.

The number of cards divisible by 24= 4

The number of cards divisible by 6=16

The number of cards divisible by 8= 12

The number of cards with numbers divisible by 8 or 6:

16+12-4= 24

And, the number of cards with numbers divisible by 6 or 8 but not 24

= 24-4 = 20 cards

Now, the probability of drawing a card divisible by 6 and 8 but not 24= 20÷100

=2÷10

=1÷5

Result:

Thus, the probability of drawing a card divisible by 6 and 8 but not 24 is 1:5.

(#SPJ2)