Question

A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears 

i. an odd number. 

ii. a complete square number.

Answer 1

Sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30} 

∴ n(S) = 30 

i. Let A be the event that the ticket drawn bears an odd number. 

∴ A = {1,3,5,7,9,11,13,15,17,19,21, 23,25,27,29}

∴ n(A) = 15

∴ P(A) = \(\frac{n(A)}{n(S)}\) = 15/30

∴  P(A) = 1/2

ii. Let B be the event that the ticket drawn bears a complete square number. 

∴ B = {1,4,9,16,25} 

∴ n(B) = 5

∴ P(B) = \(\frac{n(B)}{n(S)}\)= 5/30

∴ P(B) = 1/6

∴ P(A) = 1/2; P(B) = 1/6