Question

A bag contains cards numbers from 1 to 49. A card is drawn from the bag at random, after mixing the cards thoroughly. Find the probability that the number on the drawn card is:
(1) An odd number
(2) A multiple of 5
(3) A perfect Square
(4) An even prime number

Answer 1

Total number of cards = 49
(i) Total number of outcomes = 49
The odd numbers from 1 to 49 are 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47 and 49.
Total number of favourable outcomes = 25
$\therefore Requiredprobability=\frac{Totalnumberoffavourableoutcomes}{Totalnumberofoutcomes}=\frac{25}{49}$
(ii) Total number of outcomes = 49
The number 5,10,15,20,25,30,35,40 and 45 multiples of 5.
The number of favourable outcomes = 9
$\therefore Requiredprobability=\frac{Totalnumberoffavourableoutcomes}{Totalnumberofoutcomes}=\frac{9}{49}$
(iii) Total number of outcomes = 49
The number 1,4,9,16,25,36 and 49 are perfect squares.
Total number of favourable outcomes = 7

∴ Required probability = $\frac{Totalnumberoffavourableoutcomes}{Totalnumberofoutcomes}=\frac{7}{49}=\frac{1}{7}$

(iv)

Total number of outcomes = 49

We know that there is only one even prime number which is 2

Total number of favourable outcomes = 1

∴ Required probability = $\frac{Totalnumberoffavourableoutcomes}{Totalnumberofoutcomes}=\frac{1}{49}$