Question

Line segment JM has endpoints with coordinates 0 and 25 on a number line. Points K and L are on segment JM. K has a coordinate of 5 and point L has a coordinate of 12. Find the probability that a point on JM is placed first on JL and a second point is not placed on KL.

Answer 1

To find the probability of placing a point on segment JM first on JL and then not on KL, multiply the probability of each independent event: the probability of placing on JL (12/25) and the probability of not placing on KL within JM (18/25).

Step-by-step explanation:

The question is asking to calculate the probability of placing a point on segment JM first on JL and then a second point not on KL. We can understand this as a two-step process. First, we find the probabilities of placing a point on JL. Since the coordinates of J, K, and L are 0, 5, and 12 respectively, JL is 12 units long and JM is 25 units long, so the probability of placing a point on JL is the length of JL divided by the length of JM, which is 12/25. Second, we must find the probability of placing a point not on KL within JM. KL is 7 units long (from coordinate 5 to 12), leaving 18 units of JM that are not KL (25 - 7). The probability of not placing a point on KL is the length of JM not covered by KL divided by the total length of JM, which is 18/25.

These events are independent, so to get the overall probability of both events occurring, we multiply their probabilities: (12/25) × (18/25). This can be calculated to yield the final answer.