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Song randomly pulled a marble from a bag, recorded its color, put it back, and repeated. The results are shown in the following table.



Color
Frequency
Blue

22

Green

19

Purple

20

Red

18

Yellow

21



If Song were to repeat the experiment 25 more times, how many of those times should he expect to pull a purple marble?
Enter your answer as a number, like this: 42

1 answer

To find the expected number of times Song should pull a purple marble in 25 more trials, we first need to determine the probability of pulling a purple marble from the initial results.

  1. Calculate the total number of trials:

Total trials = Frequency of Blue + Frequency of Green + Frequency of Purple + Frequency of Red + Frequency of Yellow

Total trials = 22 + 19 + 20 + 18 + 21 = 100

  1. Calculate the probability of pulling a purple marble:

Probability of Purple = Frequency of Purple / Total trials

Probability of Purple = 20 / 100 = 0.2

  1. Use the probability to calculate the expected number of times Song should pull a purple marble in 25 more trials:

Expected number of Purple = Probability of Purple * Number of additional trials

Expected number of Purple = 0.2 * 25 = 5

Thus, Song should expect to pull a purple marble 5 times.