Question

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 placed on KL.

Answer 1

Answer:

$Probability = 0.234375$

Step-by-step explanation:

Given

JM = -2 to 14

K = Point 2

L = Point 8

Required

Determine the probability that a point is placed between JL and the second between KM

First, we need to calculate the number of points on number line JM

$JM = 14 - (-2)$

$JM = 14 +2$

$JM = 16$

This means that there are 16 points between J and M

Next, we calculate number of points between J and L

JL = -2 to 8

So:

$JL = 8 - (-2)$

$JL = 8 +2$

$JL = 10$

Next, we calculate the number of points between K and L

KL = 2 to 8

So:

$KL = 8 - 2$

$KL = 6$

The required probability is then calculated by multiplying the probability that first point lies in JL and the second lies in KL

$Probability = P(JL) * P(KL)$

Probability of JL is number of points JL divided by number of total points JM while probability of KL is number of points KL divided by number of total points JM.

So, we have:

$Probability = \frac{JL}{JM} * \frac{KL}{JM}$

$Probability = \frac{10}{16} * \frac{6}{16}$

$Probability = \frac{5}{8} * \frac{3}{8}$

$Probability = \frac{15}{64}$

$Probability = 0.234375$