Question/problem(subtask b): What is the probability of two successive random numbers has the same starting number?
What we do know is that a random number generator randomizes numbers of 6-digits independent of each other and that the generator selects a number from 1 to 9 for the first digit.
subtask a) ask us what the probability is that the phone number ending in 0 are , which I solved in the following way.
number of possible ways to choose a number of 6 digits are $$9\cdot 10\cdot...\cdot 10=9\cdot10^5$$ and number of possible to choose a number of 6 digits which have zero as ending digit(i will call this for set A) are $$9\cdot 10\cdot...\cdot 10\cdot 1=9\cdot 10^4\cdot 1=9\cdot 10^4$$
Furtherwe know that the numbers are independent of each other and therefore the random experiment is uniform probability distributed. This tells us that the probability for is number of outcomes in A divided with the all possible outcomes of phonenumbers. $$P(A)=(9\cdot 10^4)/(9\cdot 10^5)=1/10$$ But subtask b above, I have no idea how I should solve it.
Answer is 1/9.for example you take a 5 digit number then there are 9*10*10*10*10 ways then for successive number to have same digit there are 1*10*10*10*10 ways.probability is 1/9 by dividing