+1836 George has an unfair six-sided die. The probability that it rolls a 6 is $\frac{1}{2}$, and the probability that it rolls any other number is $\frac{1}{10}$. What is the expected value of the number shown when this die is rolled? Express your answer as a decimal.
+23252 (1/2) the time he rolls a 6: (1/2) x 6 = 3.
(1/10) the time he rolls a 1: (1/10) x 1 = 1/10
(1/10) the time he rolls a 2: (1/10) x 2 = 2/10
(1/10) the time he rolls a 3: (1/10) x 3 = 3/10
(1/10) the time he rolls a 4: (1/10) x 4 = 4/10
(1/10) the time he rolls a 5: (1/10) x 5 = 5/10
Sum those values: 3 + 1/10 + 2/10 + 3/10 + 4/10 + 5/10 = 4.5
Expected value is 4.5
+23252 (1/2) the time he rolls a 6: (1/2) x 6 = 3.
(1/10) the time he rolls a 1: (1/10) x 1 = 1/10
(1/10) the time he rolls a 2: (1/10) x 2 = 2/10
(1/10) the time he rolls a 3: (1/10) x 3 = 3/10
(1/10) the time he rolls a 4: (1/10) x 4 = 4/10
(1/10) the time he rolls a 5: (1/10) x 5 = 5/10
Sum those values: 3 + 1/10 + 2/10 + 3/10 + 4/10 + 5/10 = 4.5
Expected value is 4.5
