Equally Likely Outcomes

Question 1

Sam wants to play a guessing game by flipping an object once. He has two objects: Object A: a regular, fair coin – both sides are the same size. Object B: a round disc that looks like a coin, but the side labeled “Heads” covers 2/3 of the disc while the “Tails” side covers only 1/3. Which object gives equally likely outcomes, and why?

Accepted Answer

Object A, because each side is the same size so heads and tails each have the same chance.

Answer

Neither object, because a flip could land on the edge of the object.

Answer

Object B, because it still only has the two labels Heads and Tails.

Answer

Both objects, because any flip that has two possible results must be equally likely.

Question 2

At the school fair, a prize wheel is divided into three colored sections: red covers 120°, blue covers 90°, and green covers 150°. Which statement correctly tells whether the wheel’s outcomes are equally likely?

Accepted Answer

The outcomes are not equally likely because the red and green sections are larger than the blue section, giving them a higher chance.

Answer

The outcomes are equally likely because the total of the angles is 360°, so each part must be the same size.

Answer

The outcomes are equally likely because there are three colors, so each has the same chance.

Answer

The outcomes are not equally likely because the wheel is broken.

Question 3

A classroom spinner is divided into three colored sections: red covers half of the circle, blue covers one‑fourth, and green covers the remaining one‑fourth. If the spinner is spun once, are the three possible outcomes (red, blue, green) equally likely? Choose the best answer.

Accepted Answer

No, because the red section is larger than the blue and green sections.

Answer

Yes, because the spinner is fair and all colors have the same chance.

Answer

Yes, because each color appears on the spinner.

Answer

No, because the spinner is broken.

Try three questions

At the school fair, a prize wheel is divided into three colored sections: red covers 120°, blue covers 90°, and green covers 150°. Which statement correctly tells whether the wheel’s outcomes are equally likely?

A classroom spinner is divided into three colored sections: red covers half of the circle, blue covers one‑fourth, and green covers the remaining one‑fourth. If the spinner is spun once, are the three possible outcomes (red, blue, green) equally likely? Choose the best answer.

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