Question

Cards marked with numbers 13, 14, 15, ..., 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that number on the card drawn is
(i)divisible by 5
(ii)a number is a perfect square

Answer 1

SOLUTION :  

Given : Cards marked with numbers from 13 to 60

Total number of outcomes = 48

(i) Let E1 = Event of getting a number divisible by 5 .

Numbers which is divisible by 5  are = 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

Number of outcome favourable to E1 = 10

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

P(E1) = 10/48 = 5/24  

Hence, the required probability of getting a number divisible by 5 , P(E1) = 5/24 .

(ii) Let E2 = Event of getting a number which is a perfect square .

Numbers which is a perfect square  are = 16, 25, 36, 49

Number of outcome favourable to E2 = 4

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

P(E2) = 4/48 = 1/12

Hence, the required probability of getting a perfect square , P(E2) = 1/12

HOPE THIS ANSWER WILL HELP YOU ...

Answer 2

Solution:

Cards marked with numbers 13, 14, 15, ..., 60


let us think it is an A.P.,first term a = 13

Common difference d= 1

So,let us find out how many terms are in this

$60 = 13 + (n - 1)1 \\ \\ 60 - 13 = (n - 1) \\ \\ 47 = n - 1 \\ \\ n = 48$
So, total outcome = 48

1) Favourable outcomes :

Numbers divisible by 5 are 15,20,25,30,35,40,45,50,55,60

= 10

probability that number on the card drawn is
divisible by 5

=10/48

= 5/24

(ii)a number is a perfect square:

Favourable outcome : 16,25,36,49 = 4


probability that number is a perfect square

= 4/48

= 1/12

Hope it helps you