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






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