Question

A game board with 17 spaces. Start, green, green, star, quesiton mark, question mark, star, question mark, green, cat town, green, green, star, question mark, green, green, star, green, end.
Which theoretical probabilities are equal to 1/3? Check all that apply.
rolling an even number on the first roll
landing on a star space on the first roll
landing at Cat Town on the first roll
not landing on a question mark or star on the first roll
rolling a number greater than 4 on the first roll

Answer 1

Which are 1/3?:
- landing on a star on the first roll — YES
- not landing on a question mark or star on the first roll — YES
- rolling a number greater than 4 on the first roll — YES

Why: a single die roll can move you to spaces 1–6. Those spaces are:
1 green, 2 green, 3 star, 4 question, 5 question, 6 star.
So stars = 2/6 = 1/3; greens (not question or star) = 2/6 = 1/3; rolls >4 (5 or 6) = 2/6 = 1/3.
The other two are not 1/3: rolling an even number = 3/6 = 1/2; Cat Town is space 9 so probability = 0.