A bag contains 4 red, 4 blue, 4 green, and 4

yellow marbles. A marble is randomly pulled from
the bag and replaced seven times. The table shows
the outcome of the experiment.

TRIAL - OUTCOME
1 - YELLOW
2 - BLUE
3 - YELLOW
4 - RED
5 - BLUE
6 - YELLOW
7 - YELLOW

Which marble color’s observed frequency is closest
to its expected frequency

1. Red
2 Blue
3 Green
4 Yellow

Blue

Blue

Sol.
Expected= 4/16 or 1/4 chances of picking any one color.
Observed Blue 2/7 closest to Expected

Blue

To determine which marble color's observed frequency is closest to its expected frequency, we need to first calculate the expected frequency for each color and then compare it to the observed frequency.

Given that there are 4 red, 4 blue, 4 green, and 4 yellow marbles in the bag, the expected frequency for each color is 7/16 since a marble is randomly pulled from the bag and replaced seven times.

Next, we need to calculate the observed frequency for each color. Looking at the table, we can see that the observed frequencies are as follows:

- Red: 1 occurrence
- Blue: 2 occurrences
- Green: 0 occurrences
- Yellow: 4 occurrences

Now we can compare the observed frequencies to the expected frequencies:

- Red: Observed frequency = 1, Expected frequency = 7/16
- Blue: Observed frequency = 2, Expected frequency = 7/16
- Green: Observed frequency = 0, Expected frequency = 7/16
- Yellow: Observed frequency = 4, Expected frequency = 7/16

We can see that the observed frequency for yellow marbles (4 occurrences) is closest to its expected frequency (7/16), so the answer is option 4: Yellow.

yellow

Yellow