The values are: - for the black chip : x₁ = 2 - for the red chip: x₂ = -1
Let's first calculate the possibilities of each chip. There are in total 5 chips (<span>two black chips and three red chips) in the bag </span>- the possibility to draw the black chip is 2 out of 5: P₁ = 2/5 - the possibility to draw the red chip is 3 out of 5: P₂ = 3/5
In this example we have 4 different events: 1. Drawing of two black chips: P₃ = P₁ · P₁ = 2/5 · 2/5 = 4/25 2. Drawing of one black chip and then one red chip: P₄ = P₁ · P₂ = 2/5 · 3/5 = 6/25 3. Drawing of one red chip and then one black chip: P₅ = P₂ · P₁ = 3/5 · 2/5 = 6/25 5. Drawing of two black chips: P₆ = P₂ · P₂ = 3/5 <span>· 3/5 = 9/25 </span>
Therefore, <span>the expected value for each round if there are two draws per round and the chips are replaced after each draw is 0.4: P = (x</span>₁ + x₁) · P₃ + (x₁ + x₂) · P₄ + (x₁ + x₂) · P₅ + (x₂ + x₂) · P₆ P = (2+2) · 4/25 + (2-1) · 6/25 + (2-1) · 6/25 + (-1 + -1) · 9/25 P = 4 · 4/25 + 1 · 6/25 + 1 · <span>6/25</span> + -2 · <span>9/25 P = 16/25 + 6/25 + 6/25 - 18/25 P = 28/25 - 18/25 P = 10/25 = 0.4</span>
