What is the probability of two – digit number formed from the digits 2, 3, 5, 7, 9 without repeating the digits of the events? (a) the number so formed is an odd number. (b) the two – digit number so formed is a multiple of 5.

What is the probability of two – digit number formed from the digits 2, 3, 5, 7, 9 without repeating the digits of the events?

(a) the number so formed is an odd number.

(b) the two – digit number so formed is a multiple of 5.

Answer: -

The given digits are 2, 3, 5, 7 , 9 and we need to form two digits numbers without repeating the digits

Sample Space =  { 23, 25, 27, 29, 32, 35, 37, 39, 52, 53, 57, 59, 72, 73, 75, 79, 92, 93, 95, 97}

∴ n(S) = 20

(a) Let A = Event of getting an odd number.

∴ A = { 23, 25, 27, 29, 35, 37, 39, 53, 57, 59, 73, 75, 79, 93, 95, 97}

∴n(A) = 16

∴ P(A) = n(A) n(S) ∴ P(A) =    16    20 ∴ P(A) =  4  5

(b) Let B = Event of getting the two – digit number so formed is a multiple of 5.

B = { 25, 35, 75, 95}

∴ n(4) = 4

∴ P(B) = n(B) n(S) ∴ P(B) =    4    20 ∴ P(B) =  1  5