A bag contains 14 blue marbles, 10 red marbles, and 6 yellow marbles.If Henna randomly draws a marble from the bag (and puts it back) 25 times, how many times should she expect to pull a yellow marble?

Question

Enter your answer as a number, like this: 42

Answer 1

To determine the expected number of times Henna draws a yellow marble, we first need to find the total number of marbles in the bag and the probability of drawing a yellow marble.

1. Calculate the total number of marbles: \[ \text{Total marbles} = 14 \text{ (blue)} + 10 \text{ (red)} + 6 \text{ (yellow)} = 30 \]

2. Calculate the probability of drawing a yellow marble: \[ P(\text{yellow}) = \frac{\text{Number of yellow marbles}}{\text{Total number of marbles}} = \frac{6}{30} = \frac{1}{5} \]

3. Calculate the expected number of times Henna draws a yellow marble in 25 draws: \[ \text{Expected number of yellow marbles} = \text{Number of draws} \times P(\text{yellow}) = 25 \times \frac{1}{5} = 5 \]

Therefore, Henna should expect to pull a yellow marble 5 times.