[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-265394-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-265394-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","statistics-1-probability-exam-questions-pack-b","Statistics 1 Probability Exam Questions Pack B","","A set of Statistics 1 probability exam questions designed for Spec B S1 coverage. The problems address independent events and conditional probability, including cinema popcorn scenarios, birthday date probabilities within January, and availability of newspaper copies with ordered visiting strategies. Further questions use combinatorics and sampling without replacement to model tin contents after a flood, teacher service distributions by gender, and roadside lorry test outcomes. Suitable for practice and assessment on core probability 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do you find the probability of birthdays falling on specific dates in January?","Question",{"text":63,"@type":64},"Assume each friend’s birthday is equally likely across the 31 days, then multiply the relevant 1/31 terms (and use 1/31 vs 30/31 for same-day vs different-day cases).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are probabilities handled when newsagents are checked in a fixed order until an item is found?",{"text":68,"@type":64},"Compute the chance that earlier agents fail (don’t have a Chronicle) and the selected agent succeeds, then sum over the possible point of success (here specifically focusing on success at Arif).",{"name":70,"@type":61,"acceptedAnswer":71},"What approach is used for tin, teacher, lorry, and membership questions involving sampling without replacement?",{"text":72,"@type":64},"Use counting/proportions based on combinations without replacement, or use hypergeometric-style reasoning to calculate probabilities for specified numbers of items/events.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},265394,1789395201,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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who all have birthdays during January.Assuming thateach friend's birthday is equally likely to be on any one of the 31 days of January,find theprobability that:  \n(a)Shahid's birthday is on January 3rd;  \n(1 mark)  \n(b)both Shahid's and Tracy's birthdays are on January 3rd;  \n(2 marks)  \n(c)all three friends'birthdays are on the same day;  \n(2 marks)  \n(3 marks)  \n(d)all three friends'birthdays are on different days.  \n6 Denzel and Cherie are friends who often go to the cinema together.On such visits there is a probabilityof 0.4 that Denzel will buy popcorn.The probability that Cherie will buy popcorn is 0.7 if Denzel buyspopcorn and 0.35 if he does not.  \n(a)When Denzel and Cherie visit the cinema together:  \n(2 marks)  \n(i)find the probability that both buy popcorn;  \n(ii)show that the probability that neither buys popcorn is 0.39;(2 marks)  \n(iii)find the probability that exactly one of them buys popcorn.(2 marks)  \n(b)Sohaib sometimes joins Denzel and Cherie on their cinema visits.On these occasions,theprobability that Sohaib buys popcorn is 0.55 if both Denzel and Cherie buy popcorn and 0.25 ifexactly one of Denzel and Cherie buys popcorn.  \nFind the probability that when Denzel,Cherie and Sohaib visit the cinema together:  \n(2 marks)  \n(i)all three buy popcorn;  \n(ii)Cherie and Sohaib buy popcorn but Denzel does not.(2 marks)  \n7 Maurice works at home.At 2pm he decides to take a break to buy a copy of the Chroniclenewspaper.There are three nearby newsagents:Arif,Bob and Carol.However by 2pm theymay have sold all their Chronicles and so have none available.The independent probabilitiesthat they have a Chronicle available at 2 pm are:  \nArif 0.4  \nBob 0.7  \nCarol 0.25  \n(a)State the probability that Bob does not have a Chronicle available at 2 pm.   (1 mark)  \n(b)Find the probability that none of the three newsagents has a Chronicle available at 2 pm.(3 marks)  \n(c)  (i)Find the probability that Bob does not have a Chronicle available at 2pm but Arifdoes.  \n(ii)Find the probability that Carol does not have a Chronicle available at 2pm but Arifdoes.(3 marks)  \n(d)Maurice decides to visit the newsagents in turn until he obtains a Chronicle or until he hasvisited all three.He tosses a coin.If it lands heads he will visit the three newsagents inthe order Bob,Arif,Carol.If it lands tails he will visit them in the order Carol,Arif,Bob.  \nFind the probability that he will obtain a Chronicle from Arif.(3 marks)  \n7 Following a flood,120 tins were recovered from Dharmesh's corner shop.Unfortunately thewater had washed off all the labels.Of the tins,50 contained pet food,20 contained peas,35 contained beans and the rest contained soup.  \n(a)Dharmesh selects a tin at random.Find the probability that it:  \n(1 mark)  \n(i)contains soup;  \n(ii)does not contain pet food.(1 mark)  \n(b)Dharmesh selects two tins at random(without replacement).Find the probability that:  \n(2 marks)  \n(i)both contain peas;  \n(ii)one contains pet food and the other contains peas.(3 marks)  \n(c)Dharmesh selects three tins at random(without replacement).Find the probability that onecontains pet food,one contains peas and one contains beans.(3 marks)  \n(d)Find the probability that Dharmesh will have to open more than two tins before she findsone which does not contain pet food.(3 marks)  \n4 A school employs 75 teachers.The following table summarises their length of service at theschool,classified by gender.  \n\n|  | Less than 3 years   | 3 years to 8 years   | More than 8 years   |\n| --- | --- | --- | --- |\n| Female   | 12   | 20   | 13   |\n| Male   | 8   | 15   | 7   |\n\n(a)Find the probability that a randomly selected teacher:  \n(i)is female;  \n(ii)is female,given that the teacher has more than 8 years service;  \n(iii)is female,given that the teacher has less than 3 years service.(4 marks)  \n(b)State,giving a reason,whether or not the event of s","cbCaijBCYNNVbMRU","https://ap.wps.com/l/cbCaijBCYNNVbMRU","pdf",1592329,12,"English","# Probability question 5\n## Birthdays in January (Shahid, Tracy, Dwight)\n# Probability question 6\n## Cinema popcorn probabilities (Denzel, Cherie, Sohaib)\n# Probability question 7\n## Newspaper availability at 2pm (Arif, Bob, Carol)\n# Probability question 7\n## Tin contents after a flood (pet food, peas, beans, soup)\n# Probability question 4\n## Teacher length of service by gender\n# Probability question 7\n## Lorry safety test probabilities\n# Probability question 3\n## Rugby club membership by gender (adult, social, junior)","[{\"question\":\"How do you find the probability of birthdays falling on specific dates in January?\",\"answer\":\"Assume each friend’s birthday is equally likely across the 31 days, then multiply the relevant 1/31 terms (and use 1/31 vs 30/31 for same-day vs different-day cases).\"},{\"question\":\"How are probabilities handled when newsagents are checked in a fixed order until an item is found?\",\"answer\":\"Compute the chance that earlier agents fail (don’t have a Chronicle) and the selected agent succeeds, then sum over the possible point of success (here specifically focusing on success at Arif).\"},{\"question\":\"What approach is used for tin, teacher, lorry, and membership questions involving sampling without replacement?\",\"answer\":\"Use counting/proportions based on combinations without replacement, or use hypergeometric-style reasoning to calculate probabilities for specified numbers of items/events.\"}]","Statistics 1 Probability Exam Questions Pack B | PDF"]