Question

question 3 of 7
marco designs a spinner wheel that has exactly 4 red, blue, green, and yellow. he wants the spinner wheel to have a 25% chance of landing on each section. he spins the wheel 500 times. the results of the spins are shown in this table.

spinner wheel section	number of times the spinner lands in each section
blue	165
green	130
yellow	125

based on the results in this table, one of the following changes would be the best fix. which one?

• he should decrease the area of the red section by increasing the area of the blue section.
• he should increase the area of the red section by decreasing the area of the blue section.
• he should increase the area of the red section by decreasing the area of any of the other three sections.
• he should decrease the area of the blue section, and then it does not matter which section’s area is increased.

Explanation:

Step1: Calculate expected spins per section

Since there are 4 sections and a 25% chance for each, expected spins per section: \( 500 \times 0.25 = 125 \).

Step2: Analyze actual spins

• Red: 80 (less than 125)
• Blue: 165 (more than 125)
• Green: 130 (close to 125)
• Yellow: 125 (exact)

Step3: Determine necessary changes

To make red's chance 25%, its area (and thus expected spins) should increase. Blue's area is too large (spins too high), so decrease blue's area to increase red's. Green and yellow are close, but blue is the most over. So increase red's area by decreasing blue's (or others, but blue is most over). The option "He should increase the area of the red section by decreasing the area of any of the other three sections" is best as blue is over, but any over section (blue, green a bit) can be decreased. Wait, blue is 165 (41% over), green 5% over, yellow exact. So decreasing blue (most over) to give to red is best, but the option says "any of the other three" which includes blue (the most over). So this option is correct.

Answer:

He should increase the area of the red section by decreasing the area of any of the other three sections.