# probability question - help!

posted by .

Two people agree to meet at a coffee shop. They each independently pick a random moment in time between 8 a.m. and 9 a.m. and show up exactly at their selected time. But they are very impatient, and only stay for 10 minutes after when they arrive. What is the probability that they meet? Express your answer as a common fraction.

• probability question - help! -

you ask two many question but the answer is 1/6

• probability question - help! -

Gee you guys always seem to provide wrong answers to easy problems. By using geometric probability, we find the answer to be 11/36.

• probability question - help! -

11/36

• probability question - help! -

mathcounts and yea are correct

We solve the problem by graphing. Let $x$ and $y$ be the arrival times of the two people in minutes after 8 a.m., so $0 \le x,y \le 60$. Then the two people meet if and only if $|x - y| \le 10$. We graph the set of points $(x,y)$ such that $|x - y| \le 10$.

[asy]
unitsize(0.08 cm);

filldraw((0,0)--(10,0)--(60,50)--(60,60)--(50,60)--(0,10)--cycle,gray(0.7),invisible);

draw((0,0)--(60,0)--(60,60)--(0,60)--cycle);
draw((10,0)--(60,50));
draw((0,10)--(50,60));

label("$x$", (60,0), E);
label("$y$", (0,60), N);
dot("$(0,0)$", (0,0), SW);
dot("$(60,0)$", (60,0), S);
dot("$(60,60)$", (60,60), NE);
dot("$(0,60)$", (0,60), W);
dot("$(10,0)$", (10,0), S);
dot("$(60,50)$", (60,50), E);
dot("$(50,60)$", (50,60), N);
dot("$(0,10)$", (0,10), W);
[/asy]

The set of all points $(x,y)$ is a square with area $60^2 = 3600$.

The area outside the "successful" region consists of two right, isosceles triangles, with legs 50 and 50. The area of each triangle is $1/2 \cdot 50 \cdot 50 = 1250$, so the area of the "successful" region is $3600 - 2 \cdot 1250 = 1100$. Therefore, the probability that the two people meet is
$\frac{1100}{3600} = \boxed{\frac{11}{36}}.$

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### PROBABILITY

R. H. Bruskin Associates Market Research found that 40% of Americans do not think that having a college education is important to succeed in the business world. If a random sample of five Americans is s selected, find these probabilities. …
2. ### Statistics

Let x and y be the amounts of time (in minutes) that a particular commuter must wait for a train on two independently selected days. Define a new random variable w by w = x + y, the sum of the two waiting times. The set of possible …
3. ### wierd math question

Two people agree to meet at a coffee shop. They each independently pick a random moment in time between 8 a.m. and 9 a.m. and show up exactly at their selected time. But they are very impatient, and only stay for 10 minutes after when …
4. ### math

35% of North Americans do not think that college education is a contributory factor to economic success. A random sample of seven North Americans is selected. Find the probability that: a. Exactly 3 people will agree with that position …
5. ### math

35% of North Americans do not think that college education is a contributory factor to economic success. A random sample of seven North Americans is selected. Find the probability that: a. Exactly 3 people will agree with that position …
6. ### statistics

Let x and y be the amounts of time (in minutes) that a particular commuter must wait for a train on two independently selected days. Define a new random variable w by w = x + y, the sum of the two waiting times. The set of possible …
7. ### math

R. H. Bruskin Associates Market Research found that 30% of Americans do not think that having a college education is important to succeed in the business world. If a random sample of five Americans is s selected, find these probabilities. …
8. ### Math

1. A customer comes into Pierre's and orders a random assortment of 6 danish. At the time she comes in, there are 26 danish sitting out: 12 raspberry, 8 cheese, and 6 cinnamon. Assume the danish are not replaced. a) What is the probability …
9. ### Statistics

Service times for customers at a post office follow some right-skewed distribution with mean 2.91 minutes and standard deviation 1.74 minutes. (a) Can you calculate the probability that the average service time for the next two customers …
10. ### Statistics

Let x and y be the amounts of time (in minutes) that a particular commuter must wait for a train on two independently selected days. Define a new random variable w by w = x + y, the sum of the two waiting times. The set of possible …

More Similar Questions