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 a_{n} = 100

a_{n}= 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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