a We are told that Morgan, Phil, Callie, and Tyreese are sitting on the edge of a pool, in that order. Morgan is 2 feet away from Phil. Phil is 4 feet away from Callie. Callie is 3 feet away from Tyreese. We are asked to find the probability that Oscar will sit between Morgan and Phil. Let's make a graph of this situation.
For simplicity we will label M the point representing Morgan, P the point representing Phil, Callie's point will be C, and Tyreese will be represented by T.
The probability that Oscar sits in between Morgan and Phil can be thought of as the probability that a random point on this entire segment ends up between points M and P. This can be calculated using the length probability ratio. We will compare the length of the segment in between Morgan and Phil to the total length of the side of the pool.
The distance between Morgan and Phil is 2 and the total length of the side of the pool is 9. Therefore, the probability that Oscar will sit in between Morgan and Phil is 2 9.
b In this part, we are asked to find the probability that Oscar sits in between Phil and Tyreese. To do that, just like in Part A we will use the length probability ratio. Let's find the distance between Phil and Tyreese and compare it to the distance of the side of the pool.
The distance between Phil and Tyreese is 7 and the total length of the side of the pool is 9. Therefore, the probability that Oscar will sit in between Phil and Tyreese is 7 9.
