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Solve for x: x + 3 > 5 Responses x > 8 x > 8 x > 1 x > 1 x > 2 x > 2 x > 3

User HTF
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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.

User Motou
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