Final answer:
To calculate the conditional probability P(x > 12|x > 8), compare the successful outcome range (12 to 23) to the interval based on the given condition (8 to 23), leading to a probability of 11/15.
Step-by-step explanation:
To find the probability P(x > 12|x > 8), we are looking for the likelihood that the event x > 12 happens given that x > 8 has already occurred. This is a conditional probability problem where the sample space is altered based on the given information.
The question implies a uniform distribution between 8 and 23 for the variable x. To calculate the conditional probability, you compare the range of x values that satisfy both conditions (greater than 8 and greater than 12) to the range of x values that satisfy the given condition (greater than 8).
Therefore, the sample space is reduced to the interval from 8 to 23. The successful outcomes of x being greater than 12 in this interval are from 12 to 23. The length of this interval is 23 - 12 = 11. The length of the initial condition (the sample space after knowing that x is greater than 8) is 23 - 8 = 15.
The conditional probability is then calculated as the ratio of the successful outcomes to the possible outcomes in the altered sample space: P(x > 12|x > 8) = 11/15.