# Math Help - uniform probability distribution

1. ## uniform probability distribution

Goodmorning MHF!
New day, new questions...
Thanks in advance for all the help you are giving me.

Now the question:
There is a stretch of river 4 miles long. Uniform continuos distribution.
X denotes the distance in miles of an emergency from the point zero of this stretch of river. The density function is

.25 for 0<x<4
0 otherwise

The rescue team base is at the midpoint of this stretch of river. Find the probability that a given emergency arises more than 1.5 miles away from this base.
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I did F(4)- F(3.5) and then I thought I could square becasue the emergency can happen from one side or the other independently. But the result is not that on the book.

Thank you a lot.

2. Do not square that number. Double it!

3. Originally Posted by Plato
Do not square that number. Double it!

Why? I thought that
independent?----> multiply!

Why shall I sum them (since they're equal)?

4. Originally Posted by 0123
Why? I thought that
independent?----> multiply! Why shall I sum them (since they're equal)?
Because it is an OR! It is not an and.
The event happens in [0,0.5] OR in [3.5,4].
Those are disjoint so $P\left( {[0,0.5] \cup [3.5,4]} \right) = P\left( {[0,0.5]} \right) + P\left( {[3.5,4]} \right)$.

5. Originally Posted by Plato
Because it is an OR! It is not an and.
The event happens in [0,0.5] OR in [3.5,4].
Those are disjoint so $P\left( {[0,0.5] \cup [3.5,4]} \right) = P\left( {[0,0.5]} \right) + P\left( {[3.5,4]} \right)$.
Oh.. I see. thank you so much