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 not placed on KL.
5/8

25/64

8/15

15/64

please help
Anybody!!

Answer 1

Answer:

B. $\frac{25}{64}$

Step-by-step explanation:

Please find the attachment.  

We have been given that 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.

The probability that the first point is positioned on JL would be $\frac{10}{16}$ as there are total 10 points on JL as L is at point 8 and J is at point -2 so (8--2=8+2=10). Total number of points on the number line JM is (14--2=14+2=16)  

The probability that second point is not placed on KL would be:

$P(\text{The point is not on KL)}=1-\text{probability that point is on KL}$

$P(\text{The point is not on KL)}=1-\frac{\text{Total points on KL}}{\text{Total points on JM}}$

$P(\text{The point is not on KL)}=1-\frac{(8-2)}{16}$

$P(\text{The point is not on KL)}=1-\frac{6}{16}$

$P(\text{The point is not on KL)}=\frac{16-6}{16}$

$P(\text{The point is not on KL)}=\frac{10}{16}$

$\text{The probability of getting 1st point on Jl and second point is not on KL}=\frac{10}{16}\times \frac{10}{16}$

$\text{The probability of getting 1st point on Jl and second point is not on KL}=\frac{5}{8}\times \frac{5}{8}$

$\text{The probability of getting 1st point on Jl and second point is not on KL}=\frac{25}{64}$

Therefore, our desired probability will $\frac{25}{64}$ and option B is the correct choice.