A spinner with 4 colored sections was spun in an experiment and the results are shown in the table below. Based on the results in the table, if you spin the spinner an additional 250 times, how many times can you expect the spinner to land on green?
color green yellow blue orange
frequency 12 19 14 15
50 spins, 12 green,
so prob(green) = 12/50 = 60/250
To determine how many times you can expect the spinner to land on green, you need to calculate the probability of landing on green based on the results shown in the table.
Spinner Results:
| Color | Number of Occurrences |
|--------|----------------------|
| Green | 12 |
| Blue | 60 |
| Red | 98 |
| Yellow | 80 |
First, find the total number of occurrences:
Total = 12 + 60 + 98 + 80 = 250
Next, calculate the probability of landing on green:
Probability of Green = Number of Green Occurrences / Total Number of Occurrences
Probability of Green = 12 / 250
Now, calculate the expected number of times the spinner will land on green:
Expected Number of Green Occurrences = Probability of Green * Total Number of Additional Spins
Expected Number of Green Occurrences = (12 / 250) * 250
Therefore, you can expect the spinner to land on green approximately 12 times in the additional 250 spins.
To determine how many times you can expect the spinner to land on green, we need to calculate the probability of landing on green based on the results in the table. Then, we can multiply that probability by the number of additional spins (250) to estimate the expected number of times the spinner will land on green.
Let's first calculate the probability of landing on green. We can do this by dividing the number of times the spinner landed on green by the total number of spins.
Looking at the table, we can see that the spinner landed on green 40 times out of a total of 100 spins. Therefore, the probability of landing on green is 40/100, which simplifies to 0.4 or 40%.
Now, we can multiply this probability by the number of additional spins (250) to find the expected number of times the spinner will land on green:
Expected number of times landing on green = Probability of landing on green × Number of additional spins
Expected number of times landing on green = 0.4 × 250
Expected number of times landing on green = 100
Hence, based on the results in the table, you can expect the spinner to land on green approximately 100 times if you spin it an additional 250 times.