Question

In a game at an amusement park, a player can win 20 points, 25 points, or 30 points. The probability of winning these points is given in the table.
Points Probability
20 0.6
25 x
30 y

If Jenny expects to win 22.5 points by playing the game once, the value of x is ___ and the value of y is ___.

Answer 1

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