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Problems cover biased coins, replacement sampling from coloured discs, sequences of race outcomes with win/draw rules, and conditional probability in driving test attempts. Additional questions use chocolate and counter bags with multiple colours, coin mixtures with different values, and travel mode scenarios combining routes with lateness probabilities.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/probability-trees-gcse-igcse-exam-question-practice/657362/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/probability-trees-gcse-igcse-exam-question-practice/657362.png","ImageObject",300,407,{"name":92,"@type":93},"\tJames","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you complete a probability tree diagram for a biased coin?","Question",{"text":112,"@type":113},"Set up the first outcome branches with probability p for Heads and 1-p for Tails, then repeat for the second throw using the same probabilities. Multiply along each path to get probabilities for sequences.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you find the probability of exactly two Heads?",{"text":117,"@type":113},"List the two possible paths that give two Heads and sum their path probabilities. For a biased coin with probability p of Heads each time, this becomes p times p.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the method for combining probabilities when switching between different situations (e.g., travel mode and being late)?",{"text":121,"@type":113},"Use conditional probability by multiplying the probability of choosing the route (bicycle or bus) by the probability of being late given that route, then add the results for the required combined event.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657362,1793073415,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},2336474466412,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","PROBABILITY TREES  \n[ESTIMATED TIME: 75 minutes]  \nGCSE  \n(+ IGCSE) EXAM QUESTION PRACTICE  \n1. [8 marks]  \nS @-%& %* G%\\#*'2;  \nCM'& %5 %* 5M(-P&N 5M' =(-G\\#G%.%5/ 5M\\#5 %5 *M-P* B'\\#2* %* ~~ ~~23 e-(@\\#* 5M(-P* 5M' @-%& 5P%@';  \n6\\#7 9-$=.'5' 5M' =(-G\\#G%.%5/ 5('' 2%\\#8(\\#$;  \n\\%(*5 5M(-P 3'@-&2 5M(-P  \nHPJ  \n6G7 \\%&2 5M' =(-G\\#G%.%5/ 5M\\#5 5M' @-%& *M-P* B'\\#2* G-5M 5%$'*;  \n;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;  \nHIJ  \n6@7 \\%&2 5M' =(-G\\#G%.%5/ 5M\\#5 5M' @-%& *M-P* B'\\#2* \\#5 .'\\#*5-&@';  \n;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;  \nHPJ  \nContains questions which have been reproduced with the kind permission of Pearson Education Limited UK  \nQuestions compiled by:  \n@Maths4Everyone  \n2. [6 marks]  \nJim has a biased coin.  \nThe probability that Jim will throw Heads on any throw isp.  \nJim throws the coin twice.  \n(a) Complete the probability tree diagram. Give your probabilities in terms ofp.  \nFirst throw Second throw  \np  \n....................  \nHeads  \n....................  \n....................  \nHeads  \nTails  \nTails  \n....................  \n....................  \nHeads  \nTails  \n(2)  \n(b) Find an expression, in terms of p, for the probability that Jim will throw two Heads.  \n..............................................................  \n(1)  \nGiven that p = 0.8,  \n(c) work out the probability that Jim will throw exactly one Head.  \n..............................................................  \n3. [8 marks]  \nA bag contains 1 red disc, 2 blue discs and 3 green discs.  \nXanthe chooses a disc at random from the bag. She notes its colour and replaces it. Then Xanthe chooses another disc at random from the bag and notes its colour.  \n(a) Complete the probability tree diagram showing all the probabilities.  \nFirst disc Second disc  \nR  \nR  \n(3)  \n4. [5 marks]  \nLinford and Alan race against each other in a competition.  \nIf one of them wins a race, he wins the competition.  \nIf the race is a draw, they run another race.  \nThey run a maximum of three races.  \nEach time they race, the probability that Linford wins is 0.35  \nEach time they race, the probability that there is a draw is 0.05 (a) Complete the probability tree diagram.  \nrace 1 race 2  \nLinford Linford  \n0.35 wins ................. wins  \n 0.05  draw ................. draw  \n................. .................  \nAlan Alan  \nwins wins  \nrace 3  \nLinford wins  \ndraw  \nAlan  \nwins  \n(2)  \n(b) Calculate the probability that Linford wins the competition.  \n......................................................  \n(3)  \n5. [6 marks]  \n0L'(' \\#(' \\ F'\\#2* %& \\# F\\#8;  \nA-? 5L' F'\\#2* \\#(' ('2;  \nV-? 5L' F'\\#2* \\#(' OL%5';  \nG-? 5L' F'\\#2* \\#(' F.,';  \n3\\#&_\\#/ 5\\#P'* \\#5 (\\#&2-$ \\# F'\\#2 ?(-$ 5L' F\\#8 \\#&2 2-'* &-5 ('=.\\#@' %5; B' 5L'& 5\\#P'* \\#5 (\\#&2-$ \\# *'@-&2 F'\\#2 ?(-$ 5L' F\\#8;  \n6\\#7 9-$=.'5' 5L' =(-F\\#F%.%5/ 5('' 2%\\#8(\\#$;  \nColour of first bead  \nColour of second bead  \nRed  \n4 9  \n..........  \n..........  \nRed  \nWhite  \nBlue  \nRed  \n..........  \nWhite  \nBlue  \nWhite  \nBlue  \nRed  \nWhite  \nBlue  \nHPJ  \n6F7 9\\#.@,.\\#5' 5L' =(-F\\#F%.%5/ 5L\\#5-&' -? 3\\#&_\\#/)* F'\\#2* %* ('2 \\#&2 L%* -5L'( F'\\#2 %* F.,';  \n..........  \n..........  \n..........  \n..........  \n;;;;;;;;;;;;;;;;;;;;  \nHPJ  \n6. [7 marks]  \nPeter wants to pass his driving test.  \nThe probability that he passes at his first attempt is 0.7 When Peter passes his driving test, he does not take it again.  \nIf he fails, the probability that he passes at the next attempt is 0.8 (a) Complete the probability tree diagram for Peter’s first two attempts.  \nFirst attempt Second attempt  \nPass  \n0.7  \n...........  \nFail  \n(b) Calculate the probability that Peter needs exactly two attempts to pass his driving test.  \n(2)  \n..........................................  \n(2)  \n(c) Calculate the probability that Peter passes his driving test at his third or fourth attempt.  \n..........................................  \n(3)  \n7. [6 marks]  \nThere are 6 milk chocolates and 4 plain chocolates in a box. Rob takes at random a ch","cbCaid5hrllCsobe","https://ap.wps.com/l/cbCaid5hrllCsobe","pdf",770478,13,"English","# Practice questions\n## Biased coin trees\n## Replacement sampling from discs\n## Race outcomes with draws\n## Bead/colour sequences\n## Driving test attempts\n## Chocolate and counters\n## Coin value selection\n## Travel by bicycle or bus","[{\"question\":\"How do you complete a probability tree diagram for a biased coin?\",\"answer\":\"Set up the first outcome branches with probability p for Heads and 1-p for Tails, then repeat for the second throw using the same probabilities. Multiply along each path to get probabilities for sequences.\"},{\"question\":\"How do you find the probability of exactly two Heads?\",\"answer\":\"List the two possible paths that give two Heads and sum their path probabilities. For a biased coin with probability p of Heads each time, this becomes p times p.\"},{\"question\":\"What is the method for combining probabilities when switching between different situations (e.g., travel mode and being late)?\",\"answer\":\"Use conditional probability by multiplying the probability of choosing the route (bicycle or bus) by the probability of being late given that route, then add the results for the required combined event.\"}]","Probability Trees - GCSE (+ IGCSE) Exam Question Practice | PDF",1792977997,33]