Question

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:

Step1: Calculate total number of cubes

First, we find the total number of cubes in the bag. The number of striped cubes is 5, dotted is 3, white is 4, and red is 3. So total cubes \( n = 5 + 3 + 4 + 3 \)
\( n = 15 \)

Step2: Probability of drawing a red cube

The number of red cubes is 3. Probability of drawing a red cube \( P(\text{red})=\frac{\text{number of red cubes}}{\text{total number of cubes}}=\frac{3}{15}=\frac{1}{5} \)

Step3: Probability of drawing a white cube

The number of white cubes is 4. Probability of drawing a white cube \( P(\text{white})=\frac{\text{number of white cubes}}{\text{total number of cubes}}=\frac{4}{15} \)

Step4: Probability of both events (with replacement)

Since we replace the cube after drawing, the two events are independent. The probability of both events happening is the product of their individual probabilities. So \( P(\text{red then white}) = P(\text{red}) \times P(\text{white}) \)
\( P(\text{red then white})=\frac{1}{5} \times \frac{4}{15}=\frac{4}{75} \)

Answer:

\(\frac{4}{75}\)