(a)Put these words in order of probability, starting with the least likely. evens certain impossible likely(1)
(b)On the probability scale, mark with a cross (X) the probability that a fair coin lands on tails.(1)
(Total for Question 1 is 2 marks)
2
A fair six-sided dice, numbered 1 to 6, is rolled once.
(a)Write down the probability that the dice lands on the number 3.(1)
(b)Write down the probability that the dice lands on a number less than 3.(1)
(Total for Question 2 is 2 marks)
3
A letter is chosen at random from the word MATHEMATICS.
(a)Work out the probability that the letter chosen is M.(1)
(b)Work out the probability that the letter chosen is a vowel.(1)
(Total for Question 3 is 2 marks)
4
60 people were asked to name their favourite fruit. The results are shown in the table below. Apple: 24 Banana: 15 Orange: 21 One of these people is chosen at random.
(a)Work out the probability that this person's favourite fruit is banana.(1)
(b)Work out the probability that this person's favourite fruit is not orange.(1)
(Total for Question 4 is 2 marks)
5
A fair spinner has 8 equal sections. 3 sections are red, 4 sections are blue and 1 section is green. The spinner is spun once.
(a)Write down the probability that the spinner lands on green.(1)
(b)Work out the probability that the spinner lands on red or blue.(1)
(c)Work out the probability that the spinner does not land on blue.(1)
(Total for Question 5 is 3 marks)
6
A bag contains 12 counters. 5 of the counters are yellow, 4 of the counters are purple and the rest of the counters are white. A counter is taken from the bag at random.
(Total for Question 6 is 2 marks)
7
The probability that it will rain tomorrow is 0.65.
(a)Work out the probability that it will not rain tomorrow.(1)
(b)Assuming the probability stays the same, work out an estimate for the number of days without rain over the next 40 days.(2)
(Total for Question 7 is 3 marks)
8
50 people were asked whether they prefer tea or coffee. The two-way table shows some of the information.
(a)Complete the two-way table.(2)
(b)One of these 50 people is chosen at random. Work out the probability that this person is female and prefers coffee.(1)
(Total for Question 8 is 3 marks)
9
Ben plays a card game 25 times. He wins 15 of these games.
(a)Work out the relative frequency of Ben winning a game.(1)
(b)Ben is about to play the game again. Estimate the probability that Ben wins this game.(1)
(Total for Question 9 is 2 marks)
10
The probability that a biased spinner lands on red is 0.2. The spinner is spun 300 times.
(Total for Question 10 is 2 marks)
11
The probability that a train is late is 0.12.
(a)Work out the probability that a train is not late.(1)
(b)There are 250 trains in total. Work out an estimate for the number of trains that are not late.(2)
(Total for Question 11 is 3 marks)
12
A bag contains only red counters and blue counters. The ratio of red counters to blue counters is 3:5.
(a)A counter is taken from the bag at random. Work out the probability that it is blue.(2)
(b)There are 40 counters in the bag altogether. Work out the number of red counters in the bag.(2)
(Total for Question 12 is 4 marks)
13
150 raffle tickets are sold, numbered 1 to 150. Sheila buys ticket number 72. One winning ticket is chosen at random.
(a)Work out the probability that Sheila's ticket is the winning ticket.(1)
(b)Work out the probability that the winning ticket number is a multiple of 10.(2)
(Total for Question 13 is 3 marks)
14
Sara has 3 T-shirts (red, blue, green) and 2 pairs of shorts (black, white). She picks one T-shirt and one pair of shorts at random to make an outfit.
(a)List all the possible different outfits Sara could make.(2)
(b)Sara picks an outfit at random. Work out the probability that she picks the red T-shirt with the black shorts.(1)
(Total for Question 14 is 3 marks)
15
A fair coin is flipped and a fair spinner with sections numbered 1, 2 and 3 is spun.
(a)Complete the sample space diagram to show all the possible outcomes.(2)
(b)Work out the probability of getting a head and an odd number.(1)
(Total for Question 15 is 3 marks)
16
90 students in Year 10 and Year 11 each choose one of Drama, Art or Music. The two-way table shows some of the information.
(a)Complete the two-way table.(3)
(b)A student is chosen at random from Year 11. Work out the probability that this student chose Music.(1)
(Total for Question 16 is 4 marks)
17
Dan rolls a biased dice 50 times and scores a six on 20 of the rolls. Ella rolls a different biased dice 200 times and scores a six on 76 of the rolls.
(a)Work out the relative frequency of scoring a six for each dice.(2)
(b)Whose result gives the more reliable estimate of the probability of scoring a six? Give a reason for your answer.(1)
(Total for Question 17 is 3 marks)
18
The probability that Priya is late for school on any given day is 0.15.
(a)Work out the probability that Priya is not late for school.(1)
(b)There are 190 school days in the year. Work out an estimate for the number of days Priya is late.(2)
(c)Explain why your answer to part (b) is only an estimate.(1)
(Total for Question 18 is 4 marks)
Mark scheme · 2.12 Probability
Question 1
(a) B1 impossible, evens, likely, certain (all four in the correct order)
(a) Answer: impossible, evens, likely, certain
(b) B1 cross at the halfway point of the scale, oe
(b) Answer: 0.5 (halfway between 0 and 1)
Question 2
(a) B1 1/6 oe
(a) Answer: 1/6
(b) B1 1/3 oe (accept 2/6)
(b) Answer: 1/3
Question 3
(a) B1 2/11 oe
(a) Answer: 2/11
(b) B1 4/11 oe
(b) Answer: 4/11
Question 4
(a) B1 1/4 oe (accept 15/60, 0.25, 25%)
(a) Answer: 1/4
(b) B1 13/20 oe (accept 39/60, 0.65, 65%)
(b) Answer: 13/20
Question 5
(a) B1 1/8 oe
(a) Answer: 1/8
(b) B1 7/8 oe
(b) Answer: 7/8
(c) B1 1/2 oe (accept 4/8, 0.5)
(c) Answer: 1/2
Question 6
M1 12 - 5 - 4 (= 3) to find the number of white counters
A1 1/4 oe (accept 3/12, 0.25, 25%)
Answer: 1/4
Question 7
(a) B1 0.35 cao
(a) Answer: 0.35
(b) M1 0.35 x 40, ft their (a)
(b) A1 14 cao
(b) Answer: 14 days
Question 8
(a) M1 25 - 12 (= 13) or 25 - 18 (= 7), a correct method to find one missing value
(a) A1 Female Tea = 13 and Female Coffee = 7, both correct
(a) Answer: Female Tea = 13, Female Coffee = 7
(b) B1 7/50 oe, ft their (a)
(b) Answer: 7/50
Question 9
(a) B1 0.6 oe (accept 15/25, 3/5, 60%)
(a) Answer: 0.6
(b) B1 0.6 oe, ft their (a)
(b) Answer: 0.6
Question 10
M1 0.2 x 300
A1 60 cao
Answer: 60
Question 11
(a) B1 0.88 cao
(a) Answer: 0.88
(b) M1 0.88 x 250, ft their (a)
(b) A1 220 cao
(b) Answer: 220 trains
Question 12
(a) M1 3 + 5 (= 8) to find the total number of ratio parts
(a) A1 5/8 oe cao
(a) Answer: 5/8
(b) M1 40 / 8 (= 5) to find the value of one ratio part
(b) A1 15 cao
(b) Answer: 15
Question 13
(a) B1 1/150 oe
(a) Answer: 1/150
(b) M1 15 identified as the number of multiples of 10 from 1 to 150 (10, 20, ..., 150)
(b) A1 1/10 oe cao
(b) Answer: 1/10
Question 14
(a) M1 at least 4 correct, distinct outfits listed with a systematic attempt
(a) A1 all 6 outfits listed correctly with no repeats: (red,black) (red,white) (blue,black) (blue,white) (green,black) (green,white)
(a) M1 at least 4 of the 6 outcomes shown correctly
(a) A1 all 6 outcomes shown correctly: H1, H2, H3, T1, T2, T3
(a) Answer: H1, H2, H3, T1, T2, T3
(b) B1 1/3 oe (accept 2/6), ft their (a)
(b) Answer: 1/3
Question 16
(a) M1 40 - 14 - 10 (= 16) to find Year 10 Art
(a) M1 30 - 14 (= 16) to find Year 11 Drama, or a correct method for another missing value
(a) A1 all remaining values correct: Year 11 Art = 12, Year 11 Music = 22, Art total = 28, Year 11 total = 50
(a) Answer: Year 10 Art = 16; Year 11 Drama = 16, Art = 12, Music = 22, Total = 50; Art total = 28
(b) B1 11/25 oe (accept 22/50), ft their (a)
(b) Answer: 11/25
Question 17
(a) B1 Dan: 0.4 oe (accept 20/50, 2/5)
(a) B1 Ella: 0.38 oe (accept 76/200, 19/50)
(a) Answer: Dan: 0.4, Ella: 0.38
(b) B1 Ella, because her dice was rolled more times (a larger sample size gives a more reliable estimate)
(b) Answer: Ella, because she rolled the dice more times
Question 18
(a) B1 0.85 cao
(a) Answer: 0.85
(b) M1 0.15 x 190 (= 28.5)
(b) A1 awrt 29 (accept 28.5 or 28, since the number of days must be a whole number)
(b) Answer: 29 days (awrt)
(c) B1 any valid reason, e.g. the probability of 0.15 is based on past data and may not stay the same for every day, or the actual number of late days may not match the calculation exactly
(c) Answer: Because the probability 0.15 may not apply equally to every day, the actual number of late days could differ from the calculated value