Question

Two-digit numbers are formed from the digits 0,1,2,3,4 where digits are not repeated. Find the probability of the events that:

(a) The number formed is an even number.

(b) The number formed is a prime number.

Answer 1

The digits given are 0,1,2,3,4 

∵ The digits are not repeated

∴ we can form two digits numbers in the sample space

Sample Space

S ≡ {10 , 12 , 13 , 14 , 20 , 21 , 23 , 24 , 30 , 31 , 32 , 34 , 40 , 41 , 42 , 43}

∴ n(S) = 16

(a) Let A ≡ Event of getting an even number

A ≡ {10 , 12 , 14 , 20 , 24 , 30 , 32 , 34 , 40 , 42}

n(A) = 10

P(A) = `("n"("A"))/("n"("S")) = 10/16`

P(A) = `5/8`

(b) Let B ≡ Event of getting a prime number

B ≡ {13 , 23 , 31 , 41 , 43}

n(B) = 5

P(B) = `"n(B)"/"n(S)" = 5/16`