6. Two digit number are formed from the digits 0, 1, 2, 3, 4 where digits are not repeated. Find the probability of the events that :
(i) the number formed is an even number.
(ii) the number formed is greater than 40.
(iii) the number formed is prime number.
Sol. The two digit numbers that can be formed using the digits 0, 1, 2, 3, 4 without repeating digits are
∴ S = { 10, 12, 13, 14, 20, 21, 23, 24 30, 31, 32, 34, 40, 41, 42, 43 }
∴ n (S) = 16
(i) Let A be the event that the number formed is even number
A = { 10, 12, 14, 20, 24, 30, 32, 34, 40, 42 }
n (A) = 10
P (A) = n (A)/n (S)
∴ P (A) = 10/16
∴ P (A) = 5/8
(ii) Let B be the event that number formed is greater than 40
B = { 41, 42, 43 }
n (B) = 3
P (B) = n (B)/n (S)
∴ P (B) = 3/16
(iii)Let C be the event that number formed is prime number
C = { 13, 23, 31, 41, 43 }
n (C) = 5
P (C) = n (C)/n (S)
∴ P (C) = 5/16
