A fair six-sided dice is rolled once. Using one of the words impossible, unlikely, evens, likely or certain, describe the probability that it lands on a number less than 7.
(Total for Question 1 is 1 mark)
2
A fair coin is tossed once. Write down, in words, the probability that it lands on heads.
(Total for Question 2 is 1 mark)
3
Write down the probability, as a number, that a fair six-sided dice lands on a number more than 6.
(Total for Question 3 is 1 mark)
4
A bag contains only yellow balls. A ball is picked at random from the bag. Write down the probability that the ball is yellow.
(Total for Question 4 is 1 mark)
5
A spinner has 8 equal sections, numbered 1 to 8. Work out the probability that the spinner lands on a number greater than 5.
(Total for Question 5 is 2 marks)
6
Write a probability of 3/10 as (i) a decimal and (ii) a percentage.
(Total for Question 6 is 2 marks)
7
A probability is given as 0.85. Write this probability as a fraction in its simplest form, showing your working.
(Total for Question 7 is 2 marks)
8
A biased coin has probability 0.65 of landing on heads. Work out the probability that it lands on tails.
(Total for Question 8 is 2 marks)
9
A box contains only red, blue and green pens. The probability of picking a red pen at random is 0.3, and the probability of picking a blue pen is 0.45. Work out the probability of picking a green pen.
(Total for Question 9 is 2 marks)
10
A card is drawn at random from a standard 52-card pack. Write down the probability, as a fraction in its simplest form, that the card is a heart.
(Total for Question 10 is 2 marks)
11
A fair 10-sided dice, numbered 1 to 10, is rolled once. Work out the probability of rolling a multiple of 3.
(Total for Question 11 is 2 marks)
12
A weather app shows a 5% chance of rain tomorrow. Using one of the words impossible, unlikely, evens, likely or certain, describe this likelihood.
(Total for Question 12 is 1 mark)
13
A fair spinner has 4 equal sections, numbered 1 to 4. It is spun once. Write down the probability, as a decimal, that it lands on 5.
(Total for Question 13 is 1 mark)
14
A raffle sells 250 tickets, and exactly one ticket wins. Priti buys 25 of the tickets. Work out the probability that one of Priti's tickets is the winning ticket.
(Total for Question 14 is 2 marks)
15
A bag contains 40 sweets. 14 are strawberry, 11 are lime, and the rest are orange. A sweet is picked at random. Work out the probability that it is orange.
(Total for Question 15 is 3 marks)
16
A four-sided spinner has sections A, B, C and D. P(A) = 0.2, P(B) = 0.3 and P(C) = 0.25. Work out P(D), and give your answer as a percentage.
(Total for Question 16 is 3 marks)
17
A box of 60 chocolates contains only milk and dark chocolates. The probability of picking a dark chocolate at random is 2/5. Work out the number of milk chocolates in the box.
(Total for Question 17 is 3 marks)
18
Kayden tosses two fair coins. List, systematically, all the possible outcomes, then find the probability that both coins land on the same side (both heads or both tails).
(Total for Question 18 is 3 marks)
19
A charity lottery has 400 tickets. The probability that a ticket picked at random is a winning ticket is 0.03. Work out how many of the 400 tickets are winning tickets, then work out the probability, as a percentage, that a ticket is not a winning ticket.
(Total for Question 19 is 3 marks)
20
A weather forecaster says there is a 20% chance of snow on a particular day. Sanjay says: "This means there is definitely no snow that day, since 20% is a small number." Evaluate Sanjay's statement, explaining what a 20% probability actually means, and state the probability word that best describes how likely snow is.
(Total for Question 20 is 3 marks)
Mark scheme · S18D Probability Basics and the Probability Scale: Fluency and Exam Drill
Question 1
B1 certain cao
Answer: Certain
Question 2
B1 evens cao
Answer: Evens
Question 3
B1 0 cao
Answer: 0
Question 4
B1 1 cao
Answer: 1
Question 5
M1 identifies 6, 7 and 8 as the numbers greater than 5 (3 favourable outcomes)
A1 3/8 oe cao
Answer: 3/8
Question 6
B1 0.3 cao
B1 30% cao
Answer: 0.3 and 30%
Question 7
M1 85/100 seen, oe
A1 17/20 cao
Answer: 17/20
Question 8
M1 1 - 0.65, oe
A1 0.35 cao
Answer: 0.35
Question 9
M1 1 - 0.3 - 0.45, oe
A1 0.25 cao
Answer: 0.25
Question 10
M1 13/52 seen, oe
A1 1/4 cao
Answer: 1/4
Question 11
M1 identifies 3, 6 and 9 as the multiples of 3 (3 favourable outcomes)
A1 3/10 oe cao
Answer: 3/10
Question 12
B1 unlikely cao
Answer: Unlikely
Question 13
B1 0 cao
Answer: 0
Question 14
M1 25/250 seen, oe
A1 1/10 oe cao
Answer: 1/10
Question 15
M1 40 - 14 - 11 (= 15), oe
M1 15/40, oe
A1 3/8 cao
Answer: 3/8
Question 16
M1 1 - 0.2 - 0.3 - 0.25, oe
A1 0.25 cao
B1 25% cao ft
Answer: P(D) = 0.25 = 25%
Question 17
M1 2/5 x 60 (= 24), oe
M1 60 - 24, oe
A1 36 cao
Answer: 36
Question 18
M1 all 4 outcomes listed systematically: HH, HT, TH, TT
M1 identifies the 2 favourable outcomes, HH and TT
A1 1/2 oe cao
Answer: 1/2
Question 19
M1 0.03 x 400, oe
A1 12 cao
B1 97% cao ft
Answer: 12 winning tickets; 97% of tickets are not winning tickets
Question 20
B1 identifies that Sanjay's statement is incorrect
B1 a correct explanation, e.g. a probability of 20% is not zero; over many similar days, snow would occur on about 20% of them, oe
B1 unlikely cao
Answer: Sanjay is wrong. A 20% probability is a real, nonzero chance, meaning snow would occur on about 20% of many similar days; it does not rule snow out. The likelihood is best described as unlikely.