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8.11D Probability Equation Questions: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A bag contains x green counters and 3 yellow counters. The probability of drawing a green counter is 1/2. Write down the value of x.

(Total for Question 1 is 1 mark)

A bag contains 5 white counters and y black counters. The probability of drawing a black counter is 2/7. Work out y.

(Total for Question 2 is 2 marks)

A spinner has sections labelled 1, 2 and 3. It is altered so there are x sections labelled 3 and one section labelled 1 and one labelled 2. The probability of landing on 3 is 3/5. Write down an equation in x.

(Total for Question 3 is 1 mark)

A bag contains blue and red counters. There are twice as many blue counters as red counters. The probability of drawing a blue counter is 0.6. Find the number of red counters, r, or explain why no integer solution exists.

(Total for Question 4 is 2 marks)

A packet contains 4 green sweets and n orange sweets. Two sweets are chosen at random without replacement. The probability both are orange is 1/3. Form an equation and find n.

(Total for Question 5 is 3 marks)

A bag contains 6 red counters and x blue counters. One counter is chosen at random. The probability it is blue is 4/7. Work out x.

(Total for Question 6 is 2 marks)

A box contains 3 purple cards and p orange cards. Two cards are drawn at random with replacement. The probability both are purple is 9/64. Form an equation and find p.

(Total for Question 7 is 3 marks)

A game uses a bag of counters. There are a red, b blue and 2 white counters. A player wins if they draw a blue counter. The probability of winning is 1/3. Given a and b are positive integers and a = 2, find b.

(Total for Question 8 is 3 marks)

A jar contains x black sweets and 6 white sweets. Two sweets are chosen without replacement. The probability of drawing one black then one white in that order is 3/14. Form an equation and find the possible value(s) of x.

(Total for Question 9 is 3 marks)

A deck contains only cards numbered 1 to n, one of each. A card is chosen at random. The probability it is a multiple of 3 is 1/4. Find n, given n is a positive integer and the deck starts at 1.

(Total for Question 10 is 4 marks)

A bag contains red and green counters. The probability of drawing a red counter is (x + 1)/(2x + 3). If this probability equals 2/5, find x.

(Total for Question 11 is 4 marks)

A game wheel is split into equal sections. The wheel has 2 red sections, r blue sections and 1 green section. The probability of landing on blue is 1/2. Find r.

(Total for Question 12 is 3 marks)

A jar contains red, blue and yellow sweets. The probability of drawing red is (2x)/(5x + 3) and this equals 1/3. Solve for x.

(Total for Question 13 is 3 marks)

There are x black buttons and 4 white buttons in a box. Two buttons are taken at random without replacement. The probability both are white is 2/5. Find x.

(Total for Question 14 is 3 marks)

A bag contains 3 blue and 9 red counters. One counter is chosen at random. Write down the probability it is red.

(Total for Question 15 is 1 mark)

A bag contains m green counters and 1 purple counter. The probability of drawing green is 3/4. Find m.

(Total for Question 16 is 2 marks)

Mark scheme · 8.11D Probability Equation Questions: Fluency and Exam Drill

Question 1

B1 x = 3 cao
Answer: 3

Question 2

M1 form equation y/(5 + y) = 2/7 or equivalent
A1 y = 2 cao
Answer: 2

Question 3

B1 x/(x + 2) = 3/5 or equivalent
Answer: x/(x+2) = 3/5

Question 4

M1 form equation 2r/(2r + r) = 0.6 or equivalent simplifying to 2/3 = 0.6
A1 state no integer r satisfies 2/3 = 0.6 or explicitly state contradiction oe
Answer: No integer r satisfies the equation (2/3 does not equal 0.6).

Question 5

M1 form (n/(n + 4)) * ((n - 1)/(n + 3)) = 1/3 or equivalent
M1 multiply out to obtain quadratic and rearrange correctly
A1 n = 6 cao (reject negative or non-integer roots)
Answer: 6

Question 6

M1 form x/(x + 6) = 4/7 or equivalent
A1 x = 8 cao
Answer: 8

Question 7

M1 form (3/(p + 3))² = 9/64 or equivalent
M1 take square root and solve 3/(p + 3) = 3/8 leading to p + 3 = 8
A1 p = 5 cao
Answer: 5

Question 8

M1 form equation b/(a + b + 2) = 1/3 with a and b as totals
M1 substitute a = 2 to obtain b/(b + 4) = 1/3 or equivalent rearrangement
A1 b = 2 cao
Answer: 2

Question 9

M1 form x/(x + 6) * 6/(x + 5) = 3/14 or equivalent
M1 multiply out to obtain the quadratic x² - 17x + 30 = 0 (or equivalent) and factorise/solve
A1 x = 2 or x = 15 (both accepted; either value alone earns full marks)
Answer: x = 2 or x = 15 (both values satisfy the equation).

Question 10

M1 identify count of multiples of 3 as floor(n/3) and form equation floor(n/3)/n = 1/4 or reason using integer k such that number of multiples = k and k/n = 1/4
M1 use integer reasoning to set k = n/4 so n divisible by 4 and test small multiples of 4 against floor(n/3) = n/4
M1 find smallest n satisfying integer constraints or demonstrate n = 4 is valid
A1 n = 4 cao (accept n = 8, the only other value satisfying floor(n/3)/n = 1/4)
Answer: 4

Question 11

M1 form (x + 1)/(2x + 3) = 2/5 or equivalent
M1 cross-multiply to get 5(x + 1) = 2(2x + 3) and expand correctly
M1 rearrange to get linear equation and solve for x
A1 x = 1 cao
Answer: 1

Question 12

M1 form r/(2 + r + 1) = 1/2 or r/(r + 3) = 1/2
M1 solve 2r = r + 3 or equivalent rearrangement
A1 r = 3 cao
Answer: 3

Question 13

M1 form 2x/(5x + 3) = 1/3 or equivalent
M1 cross-multiply and rearrange correctly
A1 x = 3 cao
Answer: 3

Question 14

M1 form 4/(x + 4) * 3/(x + 3) = 2/5 or equivalent
M1 multiply out to get (x+4)(x+3) = 30, i.e. x² + 7x - 18 = 0, and factorise/solve
A1 x = 2 cao (reject x = -9)
Answer: 2

Question 15

B1 9/12 or 3/4 cao
Answer: 3/4

Question 16

M1 form m/(m + 1) = 3/4 or equivalent
A1 m = 3 cao
Answer: 3

Probability Equation Questions: Fluency and Exam Drill - Worksheets, Questions and Revision