Line segment JM has endpoints with coordinates -2 and 14 on a number line. Points K and L are on segment JM. K has a coordinate of 2 and point L has a coordinate of 8. Find the probability that a point on JM is placed first on JL and a second point is not placed on KL.
5/8
25/64
15/64
8/15
whats the answer ?
JM has length 16
JL has length 10
KL has length 6
so P(JL,~KL) = 10/16 * (16-6)/16 = ____
To find the probability, we need to determine the length of the line segments JL and KL, and then compare their lengths to the length of line segment JM.
The length of line segment JL can be found by subtracting the coordinates of points J and L:
JL = |J - L| = |(-2) - 8| = 10
The length of line segment KL can be found by subtracting the coordinates of points K and L:
KL = |K - L| = |2 - 8| = 6
The length of line segment JM can be found by subtracting the coordinates of J and M:
JM = |J - M| = |(-2) - 14| = 16
Now, let's calculate the probability that a point on JM is placed first on JL and a second point is not placed on KL.
The first point can be placed anywhere on JM, which has a length of 16 units.
The second point cannot be placed on KL, which has a length of 6 units.
Therefore, the probability is given by:
P = (16 - 6) / 16 = 10 / 16 = 5 / 8
So, the probability is 5/8.
To find the probability that a point on JM is placed first on JL and a second point is not placed on KL, we need to understand the proportions of the different segments on JM and JL.
Given that JM has endpoints with coordinates -2 and 14, we can first find the length of JM by subtracting the coordinates of the endpoints: 14 - (-2) = 16.
We can then find the length of segment JK, which is the difference between the coordinates of the endpoints: 2 - (-2) = 4.
Next, the length of segment KL can be found by subtracting the coordinate of K from the coordinate of L: 8 - 2 = 6.
Now, to find the probability that a point on JM is placed first on JL, we need to compare the lengths of JL and JM.
The length of JL can be found by subtracting the coordinate of J (which is -2) from the coordinate of L (which is 8): 8 - (-2) = 10.
The probability of selecting a point on JM that is placed first on JL is given by the ratio of JL to JM:
Probability(J on JL first) = Length of JL / Length of JM = 10 / 16 = 5/8.
Next, to find the probability that a second point is not placed on KL, we need to find the length of KL and compare it to the length of JM.
The probability of selecting a point on JM that is not on KL is given by the ratio of the length of JM minus the length of KL to the length of JM:
Probability(second point not on KL) = (Length of JM - Length of KL) / Length of JM = (16 - 6) / 16 = 10/16 = 5/8.
Now, to find the overall probability, we multiply the probability of the first event and the probability of the second event:
Probability = Probability(J on JL first) * Probability(second point not on KL) = (5/8) * (5/8) = 25/64.
Therefore, the probability that a point on JM is placed first on JL and a second point is not placed on KL is 25/64.