4. Alyona, Dawn and Sergei are sometimes late for school. The events \(A , D\) and \(S\) are as follows:
A Alyona is late for school
D Dawn is late for school
S Sergei is late for school The Venn diagram below shows the three events \(A , D\) and \(S\) and the probabilities associated with each region of \(D\). The constants \(p , q\) and \(r\) each represent probabilities associated with the three separate regions outside \(D\).
\includegraphics[max width=\textwidth, alt={}, center]{b29b0411-8401-420b-9227-befe25c245d8-06_624_1068_845_479}

1. Write down 2 of the events \(A , D\) and \(S\) that are mutually exclusive. Give a reason for your answer. The probability that Sergei is late for school is 0.2 . The events \(A\) and \(D\) are independent.
2. Find the value of \(r\).
   (4) Dawn and Sergei's teacher believes that when Sergei is late for school, Dawn tends to be late for school.
3. State whether or not \(D\) and \(S\) are independent, giving a reason for your answer.
   (1)
4. Comment on the teacher's belief in the light of your answer to part (c).
   (1)
   (Total for Question 4 is 7 marks) \section*{Pearson Edexcel Level 3} \section*{GCE Mathematics} \section*{Paper 2: Mechanics}

   Specimen paper Time: \(\mathbf { 3 5 }\) minutes	Paper Reference(s)
   	\(\mathbf { 8 M A 0 } / \mathbf { 0 2 }\)
   You must have: Mathematical Formulae and Statistical Tables, calculator

   Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for algebraic manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. \section*{Instructions}
   • Use black ink or ball-point pen.
   • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
   • Fill in the boxes at the top of this page with your name, centre number and candidate number.
   • Answer all the questions in Section B.
   • Answer the questions in the spaces provided - there may be more space than you need.
   • You should show sufficient working to make your methods clear. Answers without working may not gain full credit.
   • Inexact answers should be given to three significant figures unless otherwise stated.
   \section*{Information}
   • A booklet 'Mathematical Formulae and Statistical Tables' is provided.
   • There are 4 questions in this section. The total mark for Part B of this paper is 30.
   • The marks for each question are shown in brackets - use this as a guide as to how much time to spend on each question.
   \section*{Advice}
   • Read each question carefully before you start to answer it.
   • Try to answer every question.
   • Check your answers if you have time at the end.
   • If you change your mind about an answer, cross it out and put your new answer and any working underneath.