A two-digit number is to be formed from the digits 0,1,2,3. Repetition of the digits is not allowed. Complete the following activity to find the probability that th enumber so formed is (1) a prime number (2) a multiple of 4.
The sample space
`S = { 10,12,13,20,21,23,30,31,32}`
`:. n (S) = 9`
( 1) Let A be the event that the number so formed is a prime number.
Then `A = { " "}, n (A) = square `
`P(A) = ( n(A))/( n (S)) =" ______"= "______"`
(2) Let B be the event that the number so formed is a multiple of 4.
Then B `={" "}, n (B) = square `
`P (B) = ( n (B))/( n (S))="______"=" ________"`

Explanation

Activity `:`
The sample space `S = { 10,12,13,30,21,23,30,31,32 }`
`:. n(S) = 9 `

(1) `A = { 13,23,31}, n(A) = 3 `
`P(A) = ( n(A)) /(n(S))= ( 3)/( 4) = (1)/(3)`
(2) ` B = {12,20,32}, n (B) = 3 `
` P(B) = ( n (B))/( n (S)) = ( 3)/( 9) = (1)/(3)`