{\rtf1{\footer \pard\plain \s16\nowidctlpar\widctlpar\tqc\tx4153\tqr\tx8306\adjustright \fs20\lang2057\cgrid {\lang1033GCSE Maths Exambank - Copyright Heinemann © 2002\par }}\ansi\deff0{\fonttbl{\f0\fnil\fcharset0 Arial;}{\f1\froman\fprq2\fcharset0 Times New Roman;}{\f2\fswiss\fprq2\fcharset0 Arial;}{\f3\froman\fprq2\fcharset0 Times;}}{\stylesheet{ Normal;}{\s1 heading 1;}}\viewkind4\uc1\pard\lang2057\fs17 Probability\f1\fs20 \par \par \pard\nowidctlpar\lang1033 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \par \pard\keepn\s1\b\f2 Question 1\par \pard\lang2057\b0\f1 \par \pard\keepn\nowidctlpar\tx426\tx851\lang1033\fs24 A dice has six faces numbered 1, 2, 3, 4, 5 and 6.\par The dice, which is biased, is thrown 200 times and the number on the upper face \par is recorded.\par The frequencies of the numbers obtained are shown in the table.\par \par \lang2057\f0\fs17{\object\objemb{\*\objclass Word.Document.8}\objw4264\objh1080{\*\objdata 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}}}\lang1033\f1\fs24 \par \par Estimate the probability that the next time the dice is thrown it will show the \par number 3.\par \pard\nowidctlpar\fs20 \par \pard\lang2057 \par \pard\nowidctlpar\lang1033 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \par \pard\keepn\s1\b\f2 Question 2\par \pard\lang2057\b0\f1 \par \pard\keepn\nowidctlpar\tx426\tx851\lang1033\fs24 The probability of a machine being able to manufacture a component within a\par tolerance of one tenth of a millimetre is 0.995.\par \b \par (a)\tab\b0 Work out the probability of the machine \b not\b0 being able to manufacture a \par \tab component to within a tolerance of one tenth of a millimetre.\par \par Ten thousand components are manufactured in one day.\par \par \b (b)\tab\b0 Work out an estimate of how many components will be outside the tolerance \par \tab of one tenth of a millimetre.\par \fs20 \par \pard\lang2057 \par \par \pard\nowidctlpar\f0\fs17 \page\lang1033\f1\fs20 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \par \pard\keepn\s1\b\f2 Question 3\par \pard\lang2057\b0\f1 \par \pard\keepn\nowidctlpar\tx426\tx851\lang1033\fs24 Peter and Asif are both taking their driving test for a motor cycle for the first time.\par The table below gives the probabilities that they will pass the test at the first attempt \par or, if they fail the first time, the probability that they will pass at the next attempt.

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\par \b (i)\tab\b0 a total of 7,\par \b (ii)\tab\b0 a total of less than 5.\tab\b (4 marks)\par \lang1033\b0 \par \pard\lang2057\fs20 \par \pard\nowidctlpar\lang1033 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \par \pard\keepn\s1\b\f2 Question 6\par \pard\lang2057\b0\f1 \par \pard\tx425\tx850\tx7087\fs24 Tina has a biased dice.\par When she rolls it, the probability that she will get a six is 0.09.\par Tina is going to roll the biased dice \b twice\b0 .\par \par Work out the probability that she will get\par \par \b (i)\tab two\b0 sixes,\par \b (ii)\tab exactly one\b0 six.\tab\b (5 marks)\b0 \par \lang1033 \par \pard\lang2057\fs20 \par \par \pard\nowidctlpar\f0\fs17 \page\lang1033\f1\fs20 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \par \pard\keepn\s1\b\f2 Question 7\par \pard\lang2057\b0\f1 \par \pard\tx425\tx850\tx7087\fs24 Jason has 10 cups.\par 6 of the cups are Star Battle cups.\par 4 of the cups are Top Pops cups.\par On Monday Jason picks at random one cup from the 10 cups.\par On Tuesday he also picks at random one cup from the same 10 cups.\par \f3 \par \b\f1 (a)\tab\b0 Complete the probability tree diagram.\par \par \f3 \par \f0\fs17{\pict\wmetafile8\picw12776\pich5923\picwgoal7243\pichgoal3358 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\par All the underweight boxes of cereal are removed.\par All boxes that are the correct weight or overweight are put in an empty warehouse.\par A box of cereal is then selected at random from the warehouse.\par \par \b (b)\tab\b0 Work out the probability that a box of cereal selected at random from the \par \tab warehouse will be overweight.\par \tab Give your answer as a fraction in its simplest form.\tab\b (2 marks)\par \lang1033\b0 \par \pard\lang2057\fs20 \par \par \pard\nowidctlpar\f0\fs17 \page\lang1033\f1\fs20 \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \emdash \par \pard\keepn\s1\b\f2 Question 9\par \pard\lang2057\b0\f1 \par \pard\tx425\tx850\tx7087\fs24 Every day, Kevin wears either a red tie or a blue tie, chosen at random.\par \par On any day, the probability that he will wear a red tie is 0.7\par \par \b (a)\tab\b0 Complete the probability tree diagram for Monday and Tuesday.\par \par \f0\fs17{\pict\wmetafile8\picw12896\pich7278\picwgoal7311\pichgoal4126 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