Answer:
(x, y) = (0.3, 0.1)
Step-by-step explanation:
The sum of the probability numbers must be 1. That is, ...
... 0.6 + x + y = 1.0
The expected value must be 22.5. That is, ...
... 20·0.6 +25x +30y = 22.5
These two equations can be written as the system of equations ...
- 5x +5y = 2 . . . . . . the first equation in standard form
- 5x +6y = 2.1 . . . . . the second equation with 5 factored out (after subtracting 12)
Subtracting the first of these equations from the second gives ...
... (5x +6y) -(5x +5y) = (2.1) -(2)
... y = 0.1
Putting this in the very first equation above, we have ...
... 0.6 +x +0.1 = 1.0
... x = 0.3 . . . . . . . . . subtract 0.7
