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
(i)an odd number
(ii)a multiple of 5
(iii)a perfect square
(iv)an even prime number

Answer 1

SOLUTION :  

Given : Cards marked with numbers from 1 to 49

Total number of outcomes = 49

(i)Let E1 = Event of getting an odd number

Numbers which are odd number = 1,3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33,35,37,39,41,43,45,47,49

Number of outcome favourable to E1 = 25

Probability (E1) = Number of favourable outcomes / Total number of outcomes

P(E1) = 25/49

Hence, the required probability of getting an odd number , P(E1) = 25/49  .

(ii)Let E2 = Event of getting the number which is a multiple of 5

Numbers which are multiple of 5 = 5,10,15,20,25,30,45,40,45

Number of outcome favourable to E2 = 9

Probability (E2) = Number of favourable outcomes / Total number of outcomes

P(E2) = 9/49

Hence, the required probability of getting the number which is a multiple of 5, P(E2) = 9/49.

(iii)Let E3 = Event of getting a number which are perfect squares  

Numbers which are perfect squares = 1, 4, 9, 16, 25 ,35,49

Number of perfect squares = 7  

Number of outcome favourable to E3 = 7

Probability (E3) = Number of favourable outcomes / Total number of outcomes

P(E3) = 7/49 = 1/7

Hence, the required probability of getting a number which are perfect squares  ,P(E3) = 1/7 .

(iv)Let E4 = Event of getting an even prime number

Number  which is even prime number = 2

Number of outcome favourable to E4 = 1

Probability (E4) = Number of favourable outcomes / Total number of outcomes

P(E4) = 1/49

Hence, the required probability of getting an odd number , P(E4) = 1/49  .

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Answer 2

1. 25/49
2. 9/49
3.7/49 = 1/7
4. 1/49