Probability of combined events — Paper 2 · IGCSE Mathematics - International 0607

14 A bag has 3 blue balls and 7 green balls only. One ball is chosen at random and not replaced. A second ball is then chosen at random. Find the probability that both balls chosen are the same colour. Give your answer in its simplest form. … [4]

4 marks

Mark scheme: 14 8 4 48 final answer B3 for oe 15 90 3 2 7 6 or M2 for × + × 10 9 10 9 3 2 7 6 or M1 for × or × 10 9 10 9

This question in 0607/21 May/June 2017

16 The probability that it rains today is 0.3 . If it rains today, the probability that it will rain tomorrow is 0.4 . If it does not rain today, the probability that it will rain tomorrow is 0.15 . Find the probability that it will rain tomorrow. … [3]

3 marks

Mark scheme: 16 0.225 oe 3 M2 for 0.3 × 0.4 + 0.7 × 0.15 oe or M1 for 0.3 × 0.4 or 0.7 × 0.15

This question in 0607/23 Oct/Nov 2017

16 A factory makes soft centre chocolates and hard centre chocolates only. The probability that a chocolate chosen at random has a hard centre is 0.6 . Three chocolates are chosen at random. Find the probability they are all soft centre chocolates. … [3] Questions 17 and 18 are printed on the next page.

3 marks

Mark scheme: 16 [0].064 3 M2 for 0.4 3 or M1 for 0.4 soi If 0 scored SC1 for answer 0.216

This question in 0607/22 May/June 2018

16 A bag contains 4 red balls and 5 blue balls only. Two balls are chosen at random without replacement. Find the probability that the two balls chosen are different colours. … [3]

3 marks

Mark scheme: 16 40  5  3 4 5 oe M2 for × × 2 oe   72  9  9 8 4 5 or M1 for × oe 9 8

This question in 0607/21 Oct/Nov 2018

9 A bag contains 2 blue balls, 3 red balls and 5 green balls only. John takes a ball out of the bag at random. He records the colour and puts the ball back in the bag. Flavia takes a ball out of the bag at random and records the colour. Find the probability that both balls are red. … [2]

2 marks

Mark scheme: 9 0.09 oe 2 M1 for 0.3 × 0.3 oe

This question in 0607/23 May/June 2019

15 An archer fires three arrows at a target. 3 The probability that the archer hits the target with each arrow is . 5 Find the probability that the archer hits the target exactly twice. … [3]

3 marks

Mark scheme: 15 54 3 2  3  2 oe M2 for 3 ×   × oe 125  5  5 2 2  3 × or M1 for    5  5

This question in 0607/22 Oct/Nov 2019

7 Iraj travels to school either by bus or on a bicycle. The probability that he goes by bus is 0.3 . He can have lunch at home or at school. The probability that he has lunch at school is 0.6 . (a) Complete the tree diagram. School 0.6 Bus 0.3 … Home School … … Bicycle … Home [2] (b) Find the probability that Iraj travels on a bicycle to school and goes home for lunch. … [2]

4 marks

Mark scheme: 7(a) Fully correct tree diagram 2 B1 for either 0.7 or 0.4 in a correct position 0.4 0.7 0.6 0.4 7(b) 0.28 oe 2 FT their tree diagram M1 for their ( 0.7 ) × their (0.4)

This question in 0607/22 Feb/March 2021

13 A bag contains 12 discs. There are 2 red discs, 4 blue discs, 5 green discs and 1 yellow disc. A disc is chosen at random and not replaced. A second disc is then chosen at random. Find the probability that both discs are the same colour. … [3]

3 marks

Mark scheme: 13 34 17 3 2 1 4 3 5 4 or M2 for × + × + × 132 66 12 11 12 11 12 11 2 1 4 3 5 4 or M1 for × or × or × 12 11 12 11 12 11

This question in 0607/23 Oct/Nov 2021

15 A bag has 5 black counters, 4 white counters and 1 red counter. One counter is chosen at random and is replaced. A second counter is then chosen at random. Find the probability that the two counters chosen are different colours. … [4]

4 marks

Mark scheme: 15 29 58 4 5 5 4 6 1 9 or or 0.58 oe M3 for      oe 50 100 10 10 10 10 10 10 or M2 for any 2 correct 5 5 4 6 1 9 or M1 for  or  or  10 10 10 10 10 10 OR  5 4 5 1 1 4  M3 for 2         oe  10 10 10 10 10 10  or M2 for any 2 correct 5 4 5 1 1 4 or M1 for  or  or  10 10 10 10 10 10 OR 5 5 4 4 1 1 M3 for 1       10 10 10 10 10 10 5 5 4 4 1 1 or M2 for  and  and  10 10 10 10 10 10 5 5 4 4 1 1 or M1 for  or  or  10 10 10 10 10 10

This question in 0607/22 May/June 2022

12 Bag A contains balls numbered 2, 4, 4, 4. Bag B contains balls numbered 1, 1, 2, 3, 4, 4. Bag C contains balls numbered 1, 2, 3, 4. One of these three bags is chosen at random. A ball is chosen at random from this bag. Find the probability that the ball chosen is numbered 4. Give your answer as a fraction. … [3] Questions 13 and 14 are printed on the next page.

3 marks

Mark scheme: 12 16 3 1 3 1 2 1 1 oe M2 for  +  +  36 3 4 3 6 3 4 1 2 1 2 1 1 or M1 for  or  or  3 4 3 6 3 4

This question in 0607/21 Oct/Nov 2022

17 An unbiased die is numbered 2, 3, 3, 4, 5, 6. Wendy rolls the die three times. Find the probability that Wendy rolls a prime number at least twice. … [4]

4 marks

Mark scheme: 17 20 160 4 4 4 2 4 4 4 or oe M3 for 3    +   oe 27 216 6 6 6 6 6 6 4 4 2 or M2 for   6 6 6 4 4 4 or   6 6 6 4 or M1 for 6

This question in 0607/22 Feb/March 2023

14 An archer shoots three arrows at a target. 7 The probability that she hits the target with each arrow is . 10 Find the probability she hits the target exactly twice. … [3]

3 marks

Mark scheme: 14 441 3 7 7 3 M2 for 3    oe 1000 10 10 10 7 7 3 or M1 for   oe 10 10 10

This question in 0607/23 May/June 2023

9 A A B C C C D Ulrich has these cards. He picks 2 cards at random without replacement. Find the probability that both cards have the letter A. … [2]

2 marks

Mark scheme: 9 1 2 2 1 oe final answer M1 for or seen 21 7 6

This question in 0607/21 Oct/Nov 2023

13 Sara has a bag containing 4 yellow balls and 5 white balls. Sara takes a ball from the bag at random without replacement. She then takes a second ball from the bag at random. Find the probability that the two balls are different colours. … [3]

3 marks

Mark scheme: 13 5 3 4 5 nfww oe final answer M2 for   2 oe 9 9 8 4 5 or M1 for  oe 9 8

This question in 0607/21 May/June 2024

20 A box contains 2 yellow pencils, 3 blue pencils and 4 green pencils. Micah takes two pencils from the box at random without replacement. Find the probability that the pencils are both blue. … [2]

2 marks

Mark scheme: 20 6 2 3 2 oe M1 for  oe 72 9 8

This question in 0607/22 Feb/March 2025

23 Bag A Bag B Bag A contains 4 white balls and 3 black balls. Bag B contains 5 white balls and 4 black balls. (a) Ranjit picks a ball at random from Bag A and replaces it. Ranjit also picks a ball at random from Bag B and replaces it. Find the probability that the two balls are the same colour. … [3] (b) Leyla picks a ball at random from Bag A. She places it into Bag B. She then picks a ball at random from Bag B. Find the probability that the ball she picks from Bag B is black. … [3]

6 marks

Mark scheme: 23(a) 32 3  3 4   4 5  M2 for    +    63  7 9   7 9   3 4   4 5  or M1 for    or     7 9   7 9  23(b) 31 3  3 5   4 4  M2 for    +    70  7 10   7 10   3 5   4 4  or M1 for    or     7 10   7 10 

This question in 0607/23 May/June 2025

11 The numbers 1 to 20 are shown in the Venn diagram. U A 20 B 5 7 4 12 2 13 8 17 6 3 9 1 10 11 14 15 16 19 C 18 (a) List the elements of A k B . … [1] (b) Find (i) n ( A j C ) … [1] (ii) n [( A j B ) l k C ] . … [1] (c) Two of the 20 numbers are picked at random without replacement. Find the probability that (i) both numbers are in ( A j B ) l k C … [2] (ii) one number is in A but not B and the other number is in B but not A. … [3]

8 marks

Mark scheme: 11(a) 3, 4, 9, 12 1 11(b)(i) 14 1 11(b)(ii) 3 1 11(c)(i) 6 2 their 3 oe B1 for oe 380 20 11(c)(ii) 60 3 5 6 oe M2 for [2]  oe 380 20 19 5 6 6 5 or M1 for or or or 20 19 20 19

This question in 0607/21 Oct/Nov 2025