+9 Suppose I have a bag with 8 slips of paper in it. Six of these have a 1 on them and the other two have a 3 on them. How many 3's do I have to add to make the expected value at least 2.5?
+23254 If you add all the numbers on these 8 slips of paper, you get (6x1) + (2x3) = 12.
Let x be the number of slips of paper (each with a 3 on it) that you add to this group.
The total number of points on all the slips will then be 12 + 3x (since each new slip has value 3) and
the total number of slips of paper is 8 + x.
Their expected value (their average) is: [12 + 3x] / [x + 8].
To get this to be at least 2.5: [12 + 3x] / [x + 8] ≥ 2.5
Multiply: [12 + 3x] ≥ 2.5 · [x + 8]
Solving: 12 + 3x ≥ 2.5x + 20
0.5x ≥ 8
x ≥ 16
+23254 If you add all the numbers on these 8 slips of paper, you get (6x1) + (2x3) = 12.
Let x be the number of slips of paper (each with a 3 on it) that you add to this group.
The total number of points on all the slips will then be 12 + 3x (since each new slip has value 3) and
the total number of slips of paper is 8 + x.
Their expected value (their average) is: [12 + 3x] / [x + 8].
To get this to be at least 2.5: [12 + 3x] / [x + 8] ≥ 2.5
Multiply: [12 + 3x] ≥ 2.5 · [x + 8]
Solving: 12 + 3x ≥ 2.5x + 20
0.5x ≥ 8
x ≥ 16
