Question

1. gina has a bag containing 5 red, 4 yellow, and 6 blue tiles that are all the same size and shape. what is the probability of picking a red tile on the first pick, replacing it, and then randomly choosing a yellow tile on the second pick? a. 1/9 b. 3/5 c. 2/21 d. 4/45

Explanation:

Step1: Calculate total number of tiles

The total number of tiles is $5 + 4+6=15$.

Step2: Calculate probability of picking a red tile first

The probability of picking a red tile on the first pick, $P(\text{red})=\frac{\text{number of red tiles}}{\text{total number of tiles}}=\frac{5}{15}=\frac{1}{3}$.

Step3: Calculate probability of picking a yellow tile second

Since the tile is replaced, the total number of tiles remains 15. The probability of picking a yellow tile on the second pick, $P(\text{yellow})=\frac{\text{number of yellow tiles}}{\text{total number of tiles}}=\frac{4}{15}$.

Step4: Calculate combined probability

Since the two events are independent (because of replacement), the probability of both events occurring is the product of their individual probabilities. So $P = P(\text{red})\times P(\text{yellow})=\frac{1}{3}\times\frac{4}{15}=\frac{4}{45}$.

Answer:

D. $\frac{4}{45}$