**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