Question

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is  an odd number 

Answer 1

The cards are numbered from 11 to 60.
∴ Total number of outcomes = 60 − 10 = 50

The odd numbers from 11 to 60 are 11, 13, 15,..., 59.
The numbers 11, 13, 15,..., 59 are in AP.
Here, a = 11 and d = 2.
Suppose the\[\therefore a_n = 59\]
\[ \Rightarrow 11 + \left( n - 1 \right) \times 2 = 59 \left[ a_n = a + \left( n - 1 \right)d \right]\]
\[ \Rightarrow 2n + 9 = 59\]
\[ \Rightarrow 2n = 59 - 9 = 50\]
\[ \Rightarrow n = 25\]re are n terms in the AP. 

So, the favourable number of outcomes are 25.
∴ P(number on the drawn card is odd) =\[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{25}{50} = \frac{1}{2}\]