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?

Explanation:

Step1: Find total number of cubes

First, calculate the total number of cubes in the bag. We have 2 striped, 3 dotted, 4 white, and 3 red cubes. So total cubes \( n = 2 + 3 + 4 + 3 = 12 \).

Step2: Probability of drawing a white cube

The number of white cubes is 4. So the probability of drawing a white cube first, \( P(W) = \frac{4}{12}=\frac{1}{3} \).

Step3: Probability of drawing a dotted cube (without replacement)

After drawing a white cube, the total number of cubes left is \( 12 - 1 = 11 \). The number of dotted cubes is 3. So the probability of drawing a dotted cube next, \( P(D|W) = \frac{3}{11} \).

Step4: Find the compound probability

Since the events are dependent (because we don't replace the first cube), the compound probability is the product of the two probabilities. So \( P(W \text{ and } D) = P(W) \times P(D|W) = \frac{1}{3} \times \frac{3}{11} = \frac{1}{11} \).

Answer:

The probability is \(\frac{1}{11}\) and the events are dependent.