Final answer:
The probability of getting two consecutive ones in a string of 1s and 0s of length n can be calculated as (n-1) / (2n).
Step-by-step explanation:
The probability of getting two consecutive ones in a string of 1s and 0s of length n can be calculated by considering the number of possible outcomes and the number of favorable outcomes.
Let's assume that the probability of getting a one is p and the probability of getting a zero is q. The favorable outcomes are when two consecutive ones occur, which can be represented as (1,1).
To calculate the probability, we need to determine the number of ways we can arrange the numbers in the string. Since we are only interested in the position of the ones, we can ignore the zeros.
Therefore, the number of favorable outcomes is n-1, because we have n-1 places where two consecutive ones can occur in a string of length n.
The number of possible outcomes is 2n, because each digit in the string can be either a one or a zero. Therefore, the probability of getting two consecutive ones is:
p = (n-1) / (2n)