Question

a bag has 2 red balls, 2 blue balls, and 1 green ball. you win $5 for red, $10 for blue, and $15 for green. what is the expected value?

Explanation:

Step1: Find total number of balls

Total balls = 2 (red) + 2 (blue) + 1 (green) = 5

Step2: Calculate probabilities

Probability of red ($P_r$) = $\frac{2}{5}$, Probability of blue ($P_b$) = $\frac{2}{5}$, Probability of green ($P_g$) = $\frac{1}{5}$

Step3: Apply expected value formula

Expected value ($E$) = $P_r \times 5 + P_b \times 10 + P_g \times 15$
Substitute values: $E = \frac{2}{5} \times 5 + \frac{2}{5} \times 10 + \frac{1}{5} \times 15$
Simplify: $E = 2 + 4 + 3 = 9$

Answer:

9