Question

Q.) Cards marked with numbers 1, 3, 5… 49 are placed in a box and mixed thoroughly.One card is drawn from the box. Find the probability that the number on the card is :-

(i) divisible by 3
(ii) a composite number
(iii) Multiple of 3 and 5.

Answer 1

HELLO DEAR,

the total outcome = 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 = 25(total no. of outcome)

(1) p(divisible by 3) = 3,9,15,21,27,33,39,45 = 8

p(E) = 8/25

==>

(2) p(a composite no.) = 9,15,21,25,27,33,35,39,45 and 49 = 10

p(E) =10/25 = 2/5

(3) multiple of 5 and 3 = 15 and 45
                                    = 2
P(E)           = 2/25

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Given the Total number of cards = 25.

n(S) = 25.

(i) Let A be the event of getting a number that is divisible by 3;

A = {3,9,15,21,27,33,39,45}

n(A) = 8.

Therefore the required probability P(A) = n(A)/n(S)
,
                                                                  = 8/25.



(ii) Let B be the event of getting a composite number.

B = {9,15,21,25,27,33,35,39,45,49}

n(B) = 10.

Therefore the required probability P(B) = n(B)/n(S)

                                                                  = 10/25


(iii) Let C be the event of getting a number which is a multiple of 3 and 5.

C = {15,45}

n(C) = 2.

Therefore the required probability P(C) = n(C)/n(S)

                                                                  = 2/25



Hope this helps!