1. ## Probability

Sorry in advance for the broad title guys, I couldn't find an appropriate term for these two probability questions.

1. Nicole and Ashley each chose a random number between 0 and 1, inclusive. What is the probability that the positive difference of the two numbers does not exceed 0.5?

2. Bob chooses a point at random on which to stand from the region $x^2+y^2<=100$. Frank, Bill, Sam, Rick, and an infinite amount of other people stand on all of the points from the region $x^2+y^2=100$. What is the probability that the largest distance between Bob and any of the other people is 12?

Not sure where to start on either of these... Any suggestions are appreciated!

P.S. The first equation from question 2 contains a less than or equal to symbol.

2. Originally Posted by rtblue
1. Nicole and Ashley each chose a random number between 0 and 1, inclusive. What is the probability that the positive difference of the two numbers does not exceed 0.5?
Can you find the amount in the shaded area?

3. Thanks! The shaded makes up 3/4 of the total area. Any suggestions on number 2?

4. Hello, rtblue!

First, I hope I've interpreted #2 correctly . . .

$\text{2. Bob stands at a random point chosen in the region }x^2+y^2\:\le\:100$.

$\text{An infinite number of people stand on the circumference of }x^2+y^2 \:=\:100$.

$\text{What is the probability that the largest distance}$
. . $\text{between Bob and any person is 12?}$

All the action takes place on or in a circle of radius 10.

To satisfy the conditions of the problem,
. . Bob must stand on or in a concentric circle of radius 2.
. . . . [Think about it!]

Then I dare to make this conjecture:
. . the probability is the ratio of the areas of the two circles.

. . $\text{Prob} \:=\:\dfrac{4\pi}{100\pi} \:=\:\dfrac{1}{25}$

5. Originally Posted by rtblue
Sorry in advance for the broad title guys, I couldn't find an appropriate term for these two probability questions.

1. Nicole and Ashley each chose a random number between 0 and 1, inclusive. What is the probability that the positive difference of the two numbers does not exceed 0.5?
It's totally unrealistic that they can choose any number between 0 and 1. There are an infinite number of numbers that they can never choose if the choosing is to be done in a finite time interval .... (Tell your instructor the question needs to be re-worded if it's to make sense. A theoretical setting is much more appropriate).

6. Thanks Soroban! That really helped.

One thing though: I think Bob would have to stand ON a concentric circle with radius 2. I don't think he could stand inside of it, because if this were to happen, the greatest distance wouldn't be 12. So, I think we have to compare the circumference of the radius 2 circle with the area of the radius 10 circle. The answer comes out to be the same though.

Thanks again!

7. I completely agree with reply #5. Both of these questions are very poorly worded. I answered question #1 the way I know what was expected regardless of the setting.

However, as stated the answer to #2 is zero. The reason is: the ‘area’ of that circle in Soroban’s reply is zero, the actual circle itself.

Now let us change the wording slightly. “What is the probability that the largest distance between Bob and any of the other people is at most 12?” Now Soroban’s solution is perfect.