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
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.
To find the probability that the second number in the locker combination is 8, we need to first determine the total number of possible combinations.
Given that the first digit is 8, there are two choices for the second digit: it can also be 8 or any other nonzero digit. Since digits can be used twice, we have a total of 11 choices for the second digit (as there are 10 nonzero digits and 8 is already used).
To calculate the probability, we need to divide the number of favorable outcomes (the second digit being 8) by the total number of possible outcomes.
Favorable outcomes: 1 (the second digit is 8)
Total possible outcomes: 11
Therefore, the probability that the second number in the locker combination is 8 is 1/11, or approximately 0.091 (rounded to three decimal places).