Daria performed an experiment in which she randomly pulled a marble from a bag, recorded its color, put it back, and then repeated. The following table represents the number of times each color of marble was pulled.

Question

Color of Marble Frequency
Yellow 26

Green 34

Purple 18

Red 22


If Daria repeats the experiment 50 more times, how many of those times should she expect to pull a yellow marble?

Enter your answer as a number, like this: 42

Answer 1

To determine how many times Daria should expect to pull a yellow marble in the next 50 trials, we first need to find the probability of pulling a yellow marble based on her initial experiment.

The total frequency of marbles pulled in Daria's initial experiment is:

\[ 26 \text{ (yellow)} + 34 \text{ (green)} + 18 \text{ (purple)} + 22 \text{ (red)} = 100 \]

Next, we calculate the probability of pulling a yellow marble:

\[ P(\text{yellow}) = \frac{\text{Frequency of yellow}}{\text{Total frequency}} = \frac{26}{100} = 0.26 \]

Now, we can use this probability to estimate how many yellow marbles she should expect to pull in 50 more trials:

\[ \text{Expected number of yellow marbles} = P(\text{yellow}) \times \text{Number of trials} = 0.26 \times 50 = 13 \]

Thus, Daria should expect to pull a yellow marble approximately 13 times.