Question

A box contains $25$ cards numbered from $1$ to $25$. A card is drawn at random from the bad. Find the probability that the number on the drawn card is divisible by $2$ or $3$.

Answer 1

Total numbers of cards $=25$

The favourable outcome = numbers divisible by $2=\{2,4,6,8,10,12,14,16,18,20,22,24\}$

The favourable outcome = number divisible by $3=\{3,6,9,12,15,18,21,24\}$

Total number of favorable outcomes $=16$

( Note: count $6,12,18$ and $24$ are common, so consider only one set )

Probability is given by,

$P\left(A\right)$$=\frac{\text{no. of possible outcomes}}{\text{No. of total outcomes}}$

Now, $P($ drawn card is divisible by $2$ or $3)=16/25$