# 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 - Mathematics

Sum

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

#### Solution

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) =

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

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 16 Probability
Exercise 16.1 | Q 48.1 | Page 24