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
15/64
8/15

Answer 1

25/64

Explanation:

consider the events F and S :

F : «the first point is placed on JL»

S : «the second point is not placed on KL»

F∩S : «a point on JM is placed first on JL and a second point is not placed on KL»

`p\left( F\right) =(JL)/(JM) =(10)/(16) =(5)/(8)`

`p\left( \overline{S} \right) =(KL)/(JM) =(6)/(16) =(3)/(8)`

`\Longrightarrow p\left( S\right) =1-p\left( \overline{S} \right) =1-(3)/(8) =(5)/(8)`

`p\left( F\cap S\right) =p\left( F\right) * p\left( S\right) =(5)/(8) * (5)/(8) =(25)/(64)`