a locker combination has tow nonzero digits and digits can be used twice. the first number is 8.what is the probality that the second number is 8

Answer 1

Assume decimal digits, so there are 9 non-zero decimal digits [1-9].
The probability that the second digit is 8 is one choice (8) out of 9 possible digits
= 1/9.

Using conditional probability,
Let event of getting (8) = 1/9
so assuming independence of the choice of digits,
P(88)=P(8)*P(8)=(1/9)*sup2;=1/81
P(8|8)=probability the second digit is eight given the first is an eight
=P(8|8)=P(8∩8)/P(8)
=(1/81)/(1/9)
=1/9
as before.