+0  
 
0
74
2
avatar

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.

 Jun 1, 2021
 #1
avatar+2205 
+1

You can do it geometrically. 

The area of x + y <= 5 is 10.5

The total area is 18. 

10.5/18 = 21/36 = 7/12

 

=^._.^=

 Jun 1, 2021
 #2
avatar+121056 
+1

See the  graph here :  https://www.desmos.com/calculator/xkhp2wh2sd

 

The total feasible  area  is a  3 x 6  rectangle  = 18  units^2

 

The  area of  concern is  a triangle  with a  height  and base  of 3....and  a  3 x 2  rectangle

This  area   is    (3*3)/2  +  3 x 2   =  9/2  + 6   =  21 / 2

 

The probability  =    (21/2)  / 18   =      21 /  36  =    7 / 12

 

 

cool cool cool

 Jun 1, 2021

29 Online Users

avatar
avatar
avatar