Question

Tickets numbered 2, 3, 4, 5, ..., 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is
(i) an even number
(ii) a number less than 16
(iii) a number which is a perfect square
(iv) a prime number less than 40

Answer 1

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 favourable outcomes = 50​ $\left[T_n=100\Rightarrow 2+(n-1)\times 2=100,\Rightarrow n=50\right]$
∴ P (getting an even number) = $\frac{50}{100}=\frac{1}{2}$

(ii) Out of these, the numbers 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 favourable outcomes =​ 14
∴ P (getting a number less than 16) = $\frac{14}{100}=\frac{7}{50}$

(iii) Out of these, the numbers that are perfect squares = 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 favourable outcomes = 9
∴ P (getting a number that is a perfect square) = $\frac{9}{100}$

(iv) Out of these, prime numbers 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 favourable outcomes =​ 12
∴ P (getting a prime number less than 40) = $\frac{12}{100}=\frac{3}{25}$