Question

EXPLORE Each of these events has three possible outcomes. Is each outcome
on each spinner equally likely to occur? Explain.
Length of Our
Lunch Break
Treat for Our
Field Trip
Amount of Homework
for the Weekend
30 min
30 min
30 min
30 min
45
min
30
min
60 min
10 min 45 min
15 min
Popcorn
Popcorn
Muffins
Muffins
Cookies
Cookies
15 min 30 min
45
min
Make Sense and Persevere Use the fact that a circle has 360° to find the
probability of each outcome on each spinner.

Answer 1

I can help, but the spinner diagram in your message is hard to read. To decide whether the three outcomes on a spinner are equally likely and to find each outcome’s probability you need the angle (in degrees) of the sector for each outcome. Use these facts:

- A full circle is 360°.
- Probability of an outcome = (angle of its sector) / 360.
- The three outcomes are equally likely only when the three sector angles are equal (each 360° ÷ 3 = 120°), which gives probability 1/3 for each.

How to proceed:
1. If you have the diagram, read or measure the angle of each labeled sector (or count equal-size sectors).
2. Compute probability = sector angle ÷ 360 for each outcome.
3. If all three probabilities are equal, the outcomes are equally likely.

Example (illustration):
- Suppose the three sectors measure 120°, 150°, and 90°.
- Prob(outcome1) = 120/360 = 1/3.
- Prob(outcome2) = 150/360 = 5/12.
- Prob(outcome3) = 90/360 = 1/4.
These are not equal, so the outcomes are not equally likely.

If you can type the sector angles or upload/describe the three clear spinners (what angles or how many degrees or how many equal slices each label covers), I’ll compute the probabilities and say whether the outcomes are equally likely.