Question

A bag contains cards which are numbered from $2$ to $90$. A card is drawn at random from the bag. Find the probability that it bears
(i) a two digit number (ii) a number which is a perfect square

Answer 1

Solution(i):

Let $E$ be the event of drawing a two digit number from the cards numbered from $2$ to $90$

Two digit numbers from $2$ to $90=10,11,12,.....,90$
No. of favorable outcomes$=81$

Total no. of possible outcomes $=89$

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{81}{89}$

Therefore, the probability of a two digit number from the cards numbered from $2$ to $90$$=\frac{81}{89}$

Solution(ii):

Let $F$ be the event of drawing a perfect square number from the cards numbered from $2$ to $90$

Perfect square numbers from $2$ to $90=4,9,16,25,36,49,64,81$
No. of favorable outcomes$=8$

Total no. of possible outcomes $=89$

We know that, Probability $P\left(F\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{8}{89}$

Therefore, the probability of drawing a perfect square number from the cards numbered from $2$ to $90$$=\frac{8}{89}$