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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
Solution
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) =\[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{25}{50} = \frac{1}{2}\]
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