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A point (x,y) is randomly selected such that 0 <= x <= 3 and 0 <= y <= 6. What is the probability that x + y <= 5? Express your answer as a common fraction.

 Apr 12, 2021
 #1
avatar+2127 
+1

If x = 0, the chance x+ y <=5 is 1/6

If x = 3, then chance x+ y <=5 = 2/3. 

Average of 1/6 and 2/3 is 5/12. 

 

I hope that's right. :))

 

=^._.^=

 Apr 12, 2021
 #2
avatar+121004 
+1

Look at  the graph here :  https://www.desmos.com/calculator/e3xiqeprcw

 

The  total area of the region   =   3 * 6   =   18

 

The  graph of  the inequality  x + y  ≤  5    forms  a trapezoid  with  bases of  5 and 2  and a  height  of  3

 

The  area of this trapezoid =  (1/2) (3) ( 5 + 2)  =   21/2  =  10.5

 

So.....the probability  that  a point  falls into  the trapezoid  =   10.5 / 18   =  7/12

 

 

cool cool cool

 Apr 12, 2021

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