IGCSE Mathematics 0580 · Topic practice
Work through single events, combined events, tree diagrams and conditional probability. Check that the probabilities on each set of branches add up to 1.
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You’re practising 2016–2018 papers. The 2019–2026 papers, including 2026, need a plan.
Unlock from $6/mo7 The probability that Kim wins a game is 0.72 . In one year Kim will play 225 games. Work out an estimate of the number of games Kim will win. ................................................. [2]
12 P Q n ( ) = 20, n (P) = 10, n (Q) = 13 and P Q 5 n j = l ^ h . Work out P Q n k ^ h. You may use the Venn diagram to help you. P Q n k = ^ h ................................................ [2]
19 X Y Z c r b i d g a m e x s f j h k l u v w (a) Use set notation to complete the statements for the Venn diagram above. (i) c .................... X [1] (ii) .................................. = { a, m, e } [1] (iii) Y Z k = .................................. [1] (b) List the elements of X Y Z j j l ^ h . ................................................... [1] (c) Find X Z n k l ^ h. ................................................... [1]
20 (a) A box contains 3 blue pens, 4 red pens and 8 green pens only. A pen is chosen at random from the box. Find the probability that this pen is green. .............................................. [1] (b) Another box contains 7 black pens and 8 orange pens only. Two pens are chosen at random from this box without replacement. Calculate the probability that at least one orange pen is chosen. .............................................. [3]
22 Samira and Sonia each have a bag containing 20 sweets. In each bag, there are 5 red, 6 green and 9 yellow sweets. (a) Samira chooses one sweet at random from her bag. Write down the probability that she chooses a yellow sweet. ................................................... [1] (b) Sonia chooses two sweets at random, without replacement, from her bag. (i) Show that the probability that she chooses two green sweets is 38 3 . [2] (ii) Calculate the probability that the sweets she chooses are not both the same colour. ................................................... [4]
22 A group of 200 people were asked which city they would like to visit next. The table shows the results. City London Paris New York Tokyo Number of people 50 48 56 46 (a) A person from the group is chosen at random. Write down the probability that this person would like to visit either Paris or Tokyo next. ................................................. [2] (b) Two people are chosen at random from the group of 200. Find the probability that one person would like to visit London next and the other person would like to visit New York next. Give your answer as a percentage. ............................................ % [3]
23 The Venn diagram shows information about the number of elements in sets A, B and . A 20 – x 8 – x 7 x B (a) ( ) n A B 23 , = Find the value of x. x = ................................................ [3] (b) An element is chosen at random from . Find the probability that this element is in ( ) A B , l. ................................................. [2]
24 Box A and box B each contain blue and green pens only. Raphael picks a pen at random from box A and Paulo picks a pen at random from box B. The probability that Raphael picks a blue pen is 3 2 . The probability that both Raphael and Paulo pick a blue pen is 15 8 . (a) Find the probability that Paulo picks a blue pen. ................................................. [2] (b) Find the probability that both Raphael and Paulo pick a green pen. ................................................. [3]
2 The time taken for each of 120 students to complete a cooking challenge is shown in the table. Time (t minutes) 20 1 t G 25 25 1 t G 30 30 1 t G 35 35 1 t G 40 40 1 t G 45 Frequency 44 32 28 12 4 (a) (i) Write down the modal time interval. ................... 1 t G ................... [1] (ii) Write down the interval containing the median time. ................... 1 t G ................... [1] (iii) Calculate an estimate of the mean time. ......................................... min [4] (iv) A student is chosen at random. Find the probability that this student takes more than 40 minutes. ................................................. [1] (b) (i) Complete the cumulative frequency table. Time (t minutes) t G 20 t G 25 t G 30 t G 35 t G 40 t G 45 Cumulative frequency 0 44 [2] 5 (ii) On the grid, draw a cumulative frequency diagram to show this information. 20 0 10 20 30 40 50 60 70 80 90 100 110 120 t 25 30 35 Time (minutes) Cumulative frequency 40 45 [3] (iii) Find the median time. ......................................... min [1] (iv) Find the interquartile range. ......................................... min [2] (v) Find the number of students who took more than 37 minutes to complete the cooking challenge. ................................................. [2]
4 (a) The diagram shows two sets of cards. Set A 1 1 2 2 2 Set B 0 1 1 1 2 (i) Jojo chooses two cards at random from Set A without replacement. Find the probability that the two cards have the same number. ................................................ [3] (ii) Jojo replaces the two cards. Kylie then chooses one card at random from Set A and one card at random from Set B. Find the probability that the two cards have the same number. ................................................ [3] (iii) Who is the most likely to choose two cards that have the same number? Show all your working. ................................................ [1] 9 (b) Set C 4 4 5 5 5 Lena chooses three cards at random from Set C without replacement. Find the probability that the third card chosen is numbered 4. ................................................ [3]
6 (a) 8 3 5 2 4 9 12 M G D The Venn diagram above shows information about the number of students who study Music (M ), Drama (D) and Geography (G). (i) How many students study Music? ................................................ [1] (ii) How many students study exactly two subjects? ................................................ [1] (iii) Two students are chosen at random from those who study Drama. Calculate the probability that they both also study Music. ................................................ [3] (iv) In the Venn diagram above, shade M D + l. [1] (b) (i) = {x : x is an integer and x 1 10 G G } A = {x : x is even} A B 4 + ! A B 1 n + = ^ h , , A B 1 7 9 , = l ^ h " , Complete the Venn diagram below using this information. A B [4] (ii) Use your Venn diagram to complete the statement. B = {....................................................} [1]
7 The frequency table shows information about the time, m minutes, that each of 160 people spend in a library. Time (m minutes) m 0 10 1 G m 10 40 1 G m 40 60 1 G m 60 90 1 G m 90 100 1 G m 100 120 1 G Frequency 3 39 43 55 11 9 (a) (i) Find the probability that one of these people, chosen at random, spends more than 100 minutes in the library. ................................................ [1] (ii) Calculate an estimate of the mean time spent in the library. ......................................... min [4] (b) Complete the cumulative frequency table below. Time (m minutes) m 10 G m 40 G m 60 G m 90 G m 100 G m 120 G Cumulative frequency 3 42 [2] (c) On the grid opposite, draw the cumulative frequency diagram. 11 0 20 40 60 80 100 120 140 160 m 0 20 40 60 Time (minutes) Cumulative frequency 80 100 120 [3] (d) Use your cumulative frequency diagram to find (i) the median, ......................................... min [1] (ii) the interquartile range, ......................................... min [2] (iii) the 90th percentile, ......................................... min [2] (iv) the number of people who spend more than 30 minutes in the library. ................................................ [2]
7 Bag A Bag B Bag A contains 3 black balls and 2 white balls. Bag B contains 1 black ball and 3 white balls. (a) A ball is taken at random from each bag. (i) Show that a black ball is more likely to be taken from bag A than from bag B. [1] (ii) Find the probability that the two balls have different colours. .................................................. [3] 15 (b) The balls are returned to their original bags. Three balls are taken at random from bag A, without replacement. Find the probability that (i) they are all black, .................................................. [2] (ii) they are all white. .................................................. [1] (c) The balls are returned to their original bags. A ball is taken at random from bag A and its colour is recorded. This ball is then placed in bag B. A ball is then taken at random from bag B. Find the probability that the ball taken from bag B has a different colour to the ball taken from bag A. .................................................. [3]
9 The probability that it will rain tomorrow is 8 5 . If it rains, the probability that Rafael walks to school is 6 1 . If it does not rain, the probability that Rafael walks to school is 10 7 . (a) Complete the tree diagram. Rains ........ ........ ........ ........ ........ ........ Does not rain Does not walk Does not walk Walks Walks [3] (b) Calculate the probability that it will rain tomorrow and Rafael walks to school. ................................................ [2] (c) Calculate the probability that Rafael does not walk to school. ................................................ [3]
10 (a) In 2017, the membership fee for a sports club was $79.50 . This was an increase of 6% on the fee in 2016. Calculate the fee in 2016. $ ............................................... [3] (b) On one day, the number of members using the exercise machines was 40, correct to the nearest 10. Each member used a machine for 30 minutes, correct to the nearest 5 minutes. Calculate the lower bound for the number of minutes the exercise machines were used on this day. ......................................... min [2] (c) On another day, the number of members using the exercise machines (E), the swimming pool (S) and the tennis courts (T) is shown on the Venn diagram. 20 33 16 7 8 4 5 S T E (i) Find the number of members using only the tennis courts. ................................................ [1] (ii) Find the number of members using the swimming pool. ................................................ [1] (iii) A member using the swimming pool is chosen at random. Find the probability that this member also uses the tennis courts and the exercise machines. ................................................ [2] (iv) Find T E S n + , ^ ^ hh. ................................................ [1]
12 A box contains 20 packets of potato chips. 6 packets contain barbecue flavoured chips. 10 packets contain salt flavoured chips. 4 packets contain chicken flavoured chips. (a) Maria takes two packets at random without replacement. (i) Show that the probability that she takes two packets of salt flavoured chips is 38 9 . [2] (ii) Find the probability that she takes two packets of different flavoured chips. ................................................. [4] (b) Maria takes three packets at random, without replacement, from the 20 packets. Find the probability that she takes at least two packets of chicken flavoured chips. ................................................. [3]
2 The probability that Stephanie wins her next tennis match is 0.85 . Find the probability that Stephanie does not win her next tennis match. ................................................. [1]
6 The probability that Pedro scores a goal in any match is 5 2 . Calculate the probability that Pedro scores a goal in each of the next two matches. ................................................... [2]
8 Simon has two boxes of cards. In one box, each card has one shape drawn on it that is either a triangle or a square. In the other box, each card is coloured either red or blue. Simon picks a card from each box at random. The probability of picking a triangle card is t. The probability of picking a red card is r. Complete the table for the cards that Simon picks, writing each probability in terms of r and t. Event Probability Triangle and red Square and red (1 - t) r Triangle and blue Square and blue [3]
17 (a) In this Venn diagram, shade the region F G , l. F G [1] (b) = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {x: x is an odd number} B = {x: x is a square number} C = {x: x is a multiple of 3} (i) Write all the elements of in the Venn diagram below. A B C [2] (ii) Another number is included in the set . This number is in the regionA B C + + l . Write down a possible value for this number. .............................................. [1]