Two people

 

 

 

 

 

 

Question:

Two people Adam and Bryan go to the same swimming pool between 2 pm and 5 pm at a random time and each one of them swims for one hour. What is the chance of them being together in the swimming pool?

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

.

.

Solution:

I will show a method that doesn’t use calculus. Consider a 3×3 grid, mark the sides 2,3,4,5 going upward and rightward. The bottom side can represent when A gets into the pool, the left when B does. Shade the portion of the grid in which the times are within 1 of each other; this portion is 5/9 of the entire area.

Untitled drawing (2).jpg

Because there is an equal chance of any point on this graph occurring, i.e A and B get in the pool at the times represented by the coordinates of the point without preference for any certain point, the probability is 5/9.

 

 

 

 

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