There are $30$ cards, of same size in a bag on which numbers $1$ to $30$ are written. If One card is taken out of the bag at random. Then Find the probability that the number on the selected card is not divisible by 3.

Given that $30$ cards of same size in a bag on which numbers $1$ to $30$ are written. And, one card is taken out of the bag at random.

to find: Probability that the number on the selected card is not divisible by $3$.

So, Total number of possible outcomes are $30(1,2,3,…30)$

Let’s E = event of getting a number that is divisible by $3$

Therefore, the number of favorable outcomes $=10(3,6,9,12,15,18,21,24,27,30)$

Probability, P(E) = Number of favorable outcomes/ Total number of outcomes

P(E) $=10/30$

$=1/3$

Then, = Event of getting number not divisible by 3

$P(\overset{\scriptscriptstyle\rightharpoonup}{E})=1-P(E)$

$P(\overset{\scriptscriptstyle\rightharpoonup}{E})=1-\frac{1}{3}$

$=2/3$

Hence, the probability that the number on the selected card is not divisible by $3=2/3$