Question

compound probability practice
determine if each situation represents an independent or dependent probability. then find the probability.

1. a bag contains 2 striped cubes, 3 dotted cubes, 4 white cubes and 3 red cubes. what is the probability of drawing a white cube, not replacing it, and then drawing a dotted cube?

handwritten calculations

1. a bag contains 5 striped cubes, 3 dotted cubes, 4 white cubes and 3 red cubes. what is the probability of drawing a red cube, replacing it, and then drawing a white cube?

Explanation:

Problem 1:

Step 1: Find total number of cubes

Total cubes = 2 (striped) + 3 (dotted) + 4 (white) + 3 (red) = 12.

Step 2: Probability of white cube first

P(white) = $\frac{4}{12}$ (since 4 white cubes out of 12 total).

Step 3: Probability of dotted cube (no replacement)

After removing 1 white cube, total cubes = 11. Dotted cubes = 3. So P(dotted) = $\frac{3}{11}$.

Step 4: Multiply probabilities (dependent events)

P(white then dotted) = $\frac{4}{12} \times \frac{3}{11}$ = $\frac{12}{132}$ = $\frac{1}{11}$.

Step 1: Find total number of cubes

Total cubes = 5 (striped) + 3 (dotted) + 4 (white) + 3 (red) = 15.

Step 2: Probability of red cube first (with replacement)

P(red) = $\frac{3}{15}$ (3 red cubes out of 15 total).

Step 3: Probability of white cube (with replacement, so total remains 15)

P(white) = $\frac{4}{15}$.

Step 4: Multiply probabilities (independent events)

P(red then white) = $\frac{3}{15} \times \frac{4}{15}$ = $\frac{12}{225}$ = $\frac{4}{75}$.

Answer:

$\frac{1}{11}$ (dependent event)

Problem 2: