Q: Two spies A and B agree to meet at a certain place between 7pm and 8pm to exchange information. They both agree to wait for 5 minutes before they leave. What is the probability that they will meet?

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (And Everone Else!)

A: To start off you can imagine the space of time to exist on a straight line. The two spies would meet if they arrive within 5 minutes of each other. If spy A arrives at time \(x\) and spy B arrives at time \(y\) then they would meet if \(|x-y| < 5\). The inequality \(|x-y| < 5\) can be broken down as two equations

$$ x-y \lt 5 \\

y - x \lt 5 $$

The area included within the zone PQRS represents an area where the two would meet. The area of the square region is \(55 \times 55 = 3025\). The area of the lower triangle is \(\frac{1}{2}\times 50 \times 50 = 1250\). Thus the sought probability is $$ P(\text{meet}) = 1 - \frac{1250\times 2}{3025} = 17.35\% $$

Some of the best books to learn th…

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (And Everone Else!)

A: To start off you can imagine the space of time to exist on a straight line. The two spies would meet if they arrive within 5 minutes of each other. If spy A arrives at time \(x\) and spy B arrives at time \(y\) then they would meet if \(|x-y| < 5\). The inequality \(|x-y| < 5\) can be broken down as two equations

$$ x-y \lt 5 \\

y - x \lt 5 $$

The area included within the zone PQRS represents an area where the two would meet. The area of the square region is \(55 \times 55 = 3025\). The area of the lower triangle is \(\frac{1}{2}\times 50 \times 50 = 1250\). Thus the sought probability is $$ P(\text{meet}) = 1 - \frac{1250\times 2}{3025} = 17.35\% $$

Some of the best books to learn th…