Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 This box holds red, blue and green counters. Which colour is impossible to take out?
Show worked solution
There are no yellow counters, so taking one is impossible.
2 A bag holds 8 red marbles and 2 blue marbles. Write how many marbles there are altogether, and how many are red.
Show worked solution
There are 8 + 2 = 10 marbles altogether and 8 are red — so red is much more likely.
3 A spinner has 4 equal parts and 3 of them are white. How many parts are NOT white?
Show worked solution
4 − 3 = 1.
Level 2 · Core
4 Which spinner is LEAST likely to stop on white?
Show worked solution
B has only 1 white part out of 4. (D is all white, so white is certain there.)
5 Box A has 3 red out of 5 counters and box B has 3 red out of 10. Write how many counters are in box A, and how many are in box B.
Show worked solution
Box A has 5 and box B has 10. Both have 3 red, but 3 out of 5 is more than half and 3 out of 10 is less, so box A gives the better chance.
6 A box has 5 red and 5 blue counters. How many counters are there altogether?
Show worked solution
5 + 5 = 10 — so taking a red one is an even chance.
Level 3 · Challenge
7 A box holds 2 red and 6 blue counters, and one is taken out without looking.1 Taking a blue counter is likely.
2 Taking a red counter is impossible.
3 Taking a green counter is impossible.
Which statements are correct?
2 Taking a red counter is impossible.
3 Taking a green counter is impossible.
Which statements are correct?
Show worked solution
6 blue out of 8 is more than half, so blue is likely (1 ✓). Red is unlikely but still possible, not impossible (2 ✗). There is no green at all, so that really is impossible (3 ✓). 1 and 3.
8 Box A has 1 red out of 5 counters and box D has 3 red out of 5. Write how many reds box D has, and how many more reds box D has than box A.
Show worked solution
Box D has 3 reds and box A has 1, so box D has 3 − 1 = 2 more.
9 A spinner has 8 equal parts and 6 of them are white. How many parts are NOT white?
Show worked solution
8 − 6 = 2 — so white is likely, since 6 out of 8 is more than half.