Question

A bag contains cards numbered from 1 to 49. A card is drawn from the bag at random, after mixing the card thoroughly. Find the probability that the number on the drawn card is an odd number 

Answer 1

The cards are numbered from 1 to 49.
∴ Total number of outcomes = 49

The odd numbers from 1 to 49 are 1, 3, 5,..., 49.
The numbers 1, 3, 5,..., 49 are in AP.
Here, a = 1 and d = 2.
Suppose there are n terms in the AP. 

\[\therefore a_n = 49\]
\[ \Rightarrow 1 + \left( n - 1 \right) \times 2 = 49 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow 2n - 1 = 49\]
\[ \Rightarrow 2n = 49 + 1 = 50\]
\[ \Rightarrow n = 25\]

So, the favourable number of outcomes are 25. 

∴ P(number on the drawn card is odd) =

\[\frac{\text{ Favourable number of outcomes`}}{\text{ Total number of outcomes }} = \frac{25}{49}\]