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.
15 questions · official format, shuffled order
1 A bag holds 5 red, 3 blue and 4 green marbles. One marble is taken without looking. What is the probability that it is not green?
Show worked solution
5 + 3 = 8 marbles are not green. 8/12 = 2/3.
2 Two dice are rolled and the numbers are added. How many of the 36 possible outcomes give a total of 7?
Show worked solution
1+6, 2+5, 3+4, 4+3, 5+2, 6+1: 6 outcomes.
3 Which statement about this spinner is correct?
Show worked solution
Red is ½, and blue + green + yellow = ¼ + ⅛ + ⅛ = ½. So Red is as likely as all the other colours put together.
4 The chance of rain tomorrow is 0.35. Which pair gives that chance as a percentage, and the chance of no rain as a decimal?
Show worked solution
0.35 is 35 hundredths, and 1 − 0.35 = 0.65: 35% and 0.65.
5 A coin is tossed three times. How many of the possible outcomes have exactly two heads?
Show worked solution
HHT, HTH and THH: 3 outcomes.
6 A bag holds 4 black and 6 white counters. One counter is drawn — it is black — and it is not put back.1 The chance the next counter is black is 1/3.
2 The chance the next counter is white is 2/3.
3 White is now less likely than it was before.
Which statements are correct?
2 The chance the next counter is white is 2/3.
3 White is now less likely than it was before.
Which statements are correct?
Show worked solution
3/9 = 1/3 (1 ✓). 6/9 = 2/3 (2 ✓). White was 6/10 = 0.6 and is now 2/3 ≈ 0.67 — more likely, not less (3 ✗). 1 and 2.
7 A fair die is rolled 60 times. About how many times would you expect a number greater than 4?
Show worked solution
2/6 = 1/3, and 1/3 of 60 = 20.
8 A spinner has three colours. The chance of red is 0.4, and blue is twice as likely as green. What is the chance of green?
Show worked solution
1 − 0.4 = 0.6 for blue and green, split into three equal parts of 0.2. Green takes one: 0.2.
9 One of these cards is picked at random. What is the probability that it shows a prime number?
Show worked solution
2, 3 and 5 are prime; 6, 8 and 9 are not. 3/6 = 1/2.
10 Spinner A has four equal sections numbered 1 to 4; spinner B has three equal sections numbered 1 to 3. Both are spun. What is the probability that they show the same number?
Show worked solution
Matching pairs: 1-1, 2-2, 3-3 (4 has no partner). 3 out of 12 = 1/4.
11 Which of these events is the most likely?
Show worked solution
1/6 ≈ 0.17, 1/4 = 0.25, 0.3, 1/4 = 0.25, 1/5 = 0.2. The biggest is 0.3: a spinner with a 0.3 chance of red landing on red.
12 A fair six-sided die is rolled once.1 The chance of an even number is 1/2.
2 The chance of a number greater than 2 is 2/3.
3 The chance of rolling a 7 is 1/7.
Which statements are correct?
2 The chance of a number greater than 2 is 2/3.
3 The chance of rolling a 7 is 1/7.
Which statements are correct?
Show worked solution
3/6 = 1/2 (1 ✓). 4/6 = 2/3 (2 ✓). A 7 is impossible — chance 0, not 1/7 (3 ✗). 1 and 2.
13 A team's chance of winning any game is 0.375. About how many wins would you expect in 40 games?
Show worked solution
40 ÷ 8 = 5, and 3 × 5 = 15 wins.
14 A menu has 3 mains (pasta, pie, salad) and 2 desserts (cake, fruit). One main and one dessert are chosen at random. What is the probability of getting the pasta with the cake?
Show worked solution
3 × 2 = 6 equally likely pairs, and only one of them is pasta with cake: 1/6.
15 This spinner has 8 equal sections: 3 red, 3 blue and 2 green.1 Red and blue are equally likely.
2 The chance of green is 1/4.
3 The chance of not landing on red is 3/8.
Which statements are correct?
2 The chance of green is 1/4.
3 The chance of not landing on red is 3/8.
Which statements are correct?
Show worked solution
3/8 each (1 ✓). 2/8 = 1/4 (2 ✓). Not red is 5/8, not 3/8 (3 ✗). 1 and 2.