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The set explains changes across prior versions, including deletions and renumbering, and notes additions by specific administrations from July 2022 onward. The questions span core probability concepts such as inclusion-exclusion, conditional probability, independence, urn models, and scenario-based computations for percentages and joint events. Answer choices are provided for each problem.",{"@graph":69,"@context":123},[70,84,106],{"@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/society-of-actuaries-exam-p-probability-sample-questions/398880/",{"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/society-of-actuaries-exam-p-probability-sample-questions/398880.png","ImageObject",300,407,{"name":92,"@type":93},"acoobca","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What kind of material does this document provide for the Exam P Probability?","Question",{"text":113,"@type":114},"It provides representative sample probability questions intended to reflect the depth of understanding required for candidates taking the Probability (P) exam.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the document describe changes between exam versions?",{"text":118,"@type":114},"It states that questions not relevant to the syllabus effective with the September 2022 administration were deleted, questions were renumbered, and it specifies which ranges were added or deleted for later administrations.",{"name":120,"@type":111,"acceptedAnswer":121},"Are the sample questions meant to mirror the distribution of future exam topics?",{"text":122,"@type":114},"No. The document notes that the distribution of questions by topic is not intended to represent the distribution on future exams.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},398880,1790554726,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},3985747870733,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","SOCIETY OF ACTUARIES  \nEXAM P PROBABILITY  \nEXAM P SAMPLE QUESTIONS  \nThis set of sample questions includes those published on the probability topic for use with previous versions of this examination. Questions from previous versions of this document that are not relevant for the syllabus effective with the September 2022 administration have been deleted. The questions have been renumbered. Unless indicated below, no questions have been added to the version published for use with exams through July 2022.  \nSome of the questions in this study note are taken from past SOA examinations.  \nThese questions are representative of the types of questions that might be asked of candidates sitting for the Probability (P) Exam. These questions are intended to represent the depth of understanding required of candidates. The distribution of questions by topic is not intended to represent the distribution of questions on future exams.  \nQuestions 271-287 were added July 2022.  \nQuestions 288-319 were added August 2022.  \nQuestions 234-236 and 282 were deleted October 2022 .  \nQuestions 320-446 were added November 2023 .  \nCopyright 2023 by the Society of Actuaries.  \n1. A survey of a group’s viewing habits over the last year revealed the following information:  \n(i) 28% watched gymnastics  \n(ii) 29% watched baseball  \n(iii) 19% watched soccer  \n(iv) 14% watched gymnastics and baseball  \n(v) 12% watched baseball and soccer  \n(vi) 10% watched gymnastics and soccer  \n(vii) 8% watched all three sports.  \nCalculate the percentage of the group that watched none of the three sports  \nduring the last year.  \n(A) 24%  \n(B) 36%  \n(C) 41%  \n(D) 52%  \n(E) 60%  \n2. The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35% . Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work.  \nCalculate the probability that a visit to a PCP’s office results in both lab work and referral to a specialist.  \n(A) 0.05  \n(B) 0.12  \n(C) 0.18  \n(D) 0.25  \n(E) 0.35  \n3. You are given P[ A ∪ B] = 0.7 and P[ A ∪ B′] = 0.9 .  \nCalculate P [A] .  \n(A) 0.2  \n(B) 0.3  \n(C) 0.4  \n(D) 0.6  \n(E) 0.8  \n4. An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44.  \nCalculate the number of blue balls in the second urn.  \n(A) 4  \n(B) 20  \n(C) 24  \n(D) 44  \n(E) 64  \n5. An auto insurance company has 10,000 policyholders. Each policyholder is classified as  \n(i) young or old;  \n(ii) male or female; and  \n(iii) married or single.  \nOf these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classified as 1320 young males, 3010 married males, and 1400 young married persons. Finally, 600 of the policyholders are young married males.  \nCalculate the number of the company’s policyholders who are young, female, and single.  \n(A) 280  \n(B) 423  \n(C) 486  \n(D) 880  \n(E) 896  \n6. A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and, of these 312 men, 102 died from causes related to heart disease.  \nCalculate the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease.  \n(A) 0.115  \n(B) 0.173  \n(C) 0.224  \n(D) 0.327  \n(E) 0.514  \n7. An insurance company estimates that 40% of policyholders who have only an auto policy will renew next year and 60% of policyholders who have only a homeowners policy will renew next year. The company estimates that 80% of policyholders who have both an auto policy and a homeowners policy will renew at least one of those policies next year.  \nCompany rec","cbCaica5hqeirAIf","https://ap.wps.com/l/cbCaica5hqeirAIf","pdf",703723,188,"English","# General Notes\n## Updates by Administration Date\n# Practice Questions\n## Question 1-11 (Introductory Set)","[{\"question\":\"What kind of material does this document provide for the Exam P Probability?\",\"answer\":\"It provides representative sample probability questions intended to reflect the depth of understanding required for candidates taking the Probability (P) exam.\"},{\"question\":\"How does the document describe changes between exam versions?\",\"answer\":\"It states that questions not relevant to the syllabus effective with the September 2022 administration were deleted, questions were renumbered, and it specifies which ranges were added or deleted for later administrations.\"},{\"question\":\"Are the sample questions meant to mirror the distribution of future exam topics?\",\"answer\":\"No. The document notes that the distribution of questions by topic is not intended to represent the distribution on future exams.\"}]","Society of Actuaries Exam P Probability - Sample Questions | PDF",1790489651,474]