Q. 75.0( 2 Votes )

Tickets numbered

Answer :

Total numbers of elementary events are: 100

(i) Let E be the event of drawing even number ticket


The favourable numbers are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …..100


This forms an A.P where a= 2, d= 2 and an = 100


an= a + (n -1) d


100 = 2 + (n -1) 2


98/2 = n -1


49 + 1 = n


n = 50, being number of term


Then, the numbers of favourable outcomes = 50


P (even number) = P (E) = 50/100 =1/2


(ii) Let E be the event of drawing number less than 16


The favourable numbers are: 2, 3, 4, 5, 6, …… 15


Then, the number of favourable outcomes = 14


P (number > 6) = P (E)= 14/100 = 7/50


(iii) let E be the event of drawing a perfect square number


The favourable numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100


The numbers of favourable outcomes = 10


P (perfect square number) = P (E) = 10/ 100 = 1/10


(iv) let E be the event of drawing prime number less than 40


The favourable numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37


Then, the numbers of favourable outcomes = 12


P (prime number less than 40) = P (E) = 12/100 = 3/25


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