Questions: Question 36 A person will randomly win 1 of 5 prizes. The cash values of the 5 prizes are 5, 10, 10, 10, 20, respectively. Which properly calculates the expected value of the person's winning prize? (A) Most common value is 10, so 10 (B) (5+10+20) / 3= 11.7 (C) 5 ×(1 / 5)+10 ×(1 / 5)+20 ×(1 / 5)= 7 (D) 5 ×(1 / 5)+10 ×(3 / 5)+20 ×(1 / 5)= 11

Solution Steps

The cash values of the prizes are given as: v_1 = 5, v_2 = 10, v_3 = 10, v_4 = 10, v_5 = 20. The probabilities of winning each prize are given as: p_1 = 0.2, p_2 = 0.2, p_3 = 0.2, p_4 = 0.2, p_5 = 0.2.

The expected value contribution of each prize is calculated as follows: $$E_i = v_1 \times p_1 = 5 \times 0.2 = 1, v_2 \times p_2 = 10 \times 0.2 = 2, v_3 \times p_3 = 10 \times 0.2 = 2, v_4 \times p_4 = 10 \times 0.2 = 2, v_5 \times p_5 = 20 \times 0.2 = 4$$

The total expected value is calculated by summing these contributions: $$E = \sum_{i=1}^{n} (v_i \times p_i) = (5 \times 0.2) + (10 \times 0.2) + (10 \times 0.2) + (10 \times 0.2) + (20 \times 0.2) = 11$$

Final Answer: