Question

Geometry

15 pts
answer is in fractions

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

216/225 is the answer

Answer 2

On a Number Line, if only whole numbers are marked

Points J, M, K, and L are marked, having coordinates 0, 25, 5, and 12.

Two points are again marked on the number line.

Probability,that a point on J M is placed first on J L

= There are 10 natural numbers in between J L and 12 natural numbers between L M.

So, Required Probability

`=\frac{_(1)^(C)\textrm{10}*_(1)^(C)\textrm{12}}{_(1)^(C)\textrm{25}*_(1)^(C)\textrm{25}}\\\\=(10*12)/(25*25)\\\\=(120)/(625)\\\\=(24)/(125)`

Now, Probability that second point is not placed on KL, it means that point is either is on J K or L M.

There are 4 natural number between 0 and 5 and 12 natural number between L and M.

Probability of marking second point on J M is

`=\frac{_(1)^(C)\textrm{4}*_(1)^(C)\textrm{12}}{_(1)^(C)\textrm{25}*_(1)^(C)\textrm{25}}\\\\=(4*12)/(25*25)\\\\=(48)/(625)`

Probability of marking two points on the number line, with given condition is

`=(120)/(625)+(48)/(625)\\\\=(168)/(625)`

If you consider ,points on the number line which are real numbers, then we can't find the required Probability that is marking two points on the line segment.