All possible outcomes are 2, 3, 4, 5,......, 101
Number of all possible outcomes = 100
(i) Out of these the numbers that are even = 2, 4, 6, 8,......,100
Let E1 be the event of getting an even number.
Then, number of favorable outcomes = 50
Tn = 100
⇒ 2 + (n - 1) x 2 = 100,
⇒ n = 50
therefore, P(getting an even number) = \(\frac{50}{100}\) = \(\frac{1}{2}\)
(ii) Out of these, number that are less than 16 = 2, 3, 4, 5,.......,15.
Let E2 be the event of getting a number less than 16.
Then, number of favorable outcomes = 14
therefore, P(getting a number less than 16) = \(\frac{14}{100}\) = \(\frac{7}{50}\)
(iii) Out of these, number that are perfect square = 4, 9, 16, 25, 36, 49, 64, 81 and 100
Let E3 be the event of getting a number that is a perfect square.
Then, number of favorable outcomes = 9
therefore, P(getting a number that is a perfect square) = \(\frac{9}{100}\)
(iv) Out of these, prime number less than 40 = 2,3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.
Let E4 be the event of getting a prime number less than 40.
Then, number of favorable outcomes = 12
Therefore, P(getting a prime number less than 40) = \(\frac{12}{100}\) = \(\frac{3}{25}\)