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Includes classwork multiple-choice prompts.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/chang-learning-shsat-lesson-25-probability-of-events/274415/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/chang-learning-shsat-lesson-25-probability-of-events/274415.png","ImageObject",300,407,{"name":42,"@type":43},"Chumphorn","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",23,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is a sample space in probability, and why is it useful?","Question",{"text":63,"@type":64},"A sample space lists all possible events/outcomes for a given experiment. It helps verify probabilities by enumerating the complete set of outcomes.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you find probabilities for four fair coin tosses?",{"text":68,"@type":64},"Model the outcomes using a full sample space and count favorable results. Then convert the count into a probability out of 16 total outcomes (for four coins).",{"name":70,"@type":61,"acceptedAnswer":71},"How are probabilities handled for spinners and dice in this lesson?",{"text":72,"@type":64},"For a spinner, probabilities come from counting labeled equally likely sectors. 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As basic examples, coins, throwing dice, a deck of cards, spinners, each have a discrete number of possible outcomes. We can study the theoretical probabilities before running experiments to verify the predicted final results.  \nIn fields such as biology, knowing the genetic alleles of a plant or vegetable correctly can then result in proper proportions of desired crops. A farmer can choose seeds that create 25% yellow healthy peapods, and 70% green ones based on the theoretical compositions ofthe genetics within the seeds.  \nIn game theory, simulations of games or events of choice can be mapped also with “sample spaces”which are a map of all possible events from the given materials in the experiment.  \n\n| Coins\u003Cbr>Possible Outcomes from a coin toss: {H,T}\u003Cbr>Sample Space 24 = 16 􀕍􀕞􀕍􀕖􀕜􀕛\u003Cbr>4 Heads, 0 Tails H H H H 3 Heads, 1 Tail H H H T H H T H H T H H T H H H 2 Heads, 2 Tails H H T T H T H T H T T H T H H T T H T H T T H H 1 Head, 3 Tails T T T H T T H T T H T T H T T T 0 Heads, 4 Tails T T T T The table on the left is a map of all possible outcomes from tossing 4 coins ina probability experiment.\u003Cbr>This is useful to see that for each toss the outcome has two, and only two, possible results. We call these types of events BINOMIAL PROBABILITY events.\u003Cbr>For each “fair” coin the probability of:\u003Cbr>“Heads” = 􀔶 = 1/2 = 50%“Tails” = 􀕂 = 1/2 = 50%\u003Cbr>The distribution shows that it is much rarer to have all 4 coins the same than different. The total PDF:\u003Cbr>Heads 4 3 2 1 0 Tails 0 1 2 3 4 Probability 1 4\u003Cbr>16 6 4\u003Cbr>16 1\u003Cbr>16 16 16\u003Cbr>The 2009 Lincoln Penny featured 4\u003Cbr>collectable designs on the reverse side.\u003Cbr>| Four coins are tossed. What are the following probabilities ?\u003Cbr>Q1: P(4 tails) ?\u003Cbr> 1 􀕍􀕞􀕍􀕖􀕜   1 =\u003Cbr>16 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 16\u003Cbr>Q2: P(3 heads) ?\u003Cbr> 4 􀕍􀕞􀕍􀕖􀕜􀕛   1 =\u003Cbr>16 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 4\u003Cbr>Q3: P(2 or more heads) ?\u003Cbr> (1 + 4 + 6) 􀕍􀕞􀕍􀕖􀕜􀕛   11 \u003Cbr>=\u003Cbr>16 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 16\u003Cbr>The sample space is a list of all possible events.\u003Cbr>The list on the left has all 16 possible tosses with 4 coins. |\n| --- | --- |\n\nName: Date:  \nChang Learning SHSAT Lesson 25: Probability of Events  \nSpinners are usually circle shaped, 2 dimensional tools for random events. With a flick of the 4 finger, an arrow spins and lands in a labeled section of the circle. Also, The spaces themselves can be unique or repeat for various probabilities. Also, they can be equally spaced, or have sectors with different angle measures.  \n\n| A spinner pictured at right, ontop, has 8 equal sections. What are the following probabilities ?\u003Cbr>Q1: P(Number 2) ?\u003Cbr> 1 􀕍􀕞􀕍􀕖􀕜􀕛   1 =\u003Cbr>8 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 8\u003Cbr>Q2: P(Odd Number) ?\u003Cbr> 4 􀕍􀕞􀕍􀕖􀕜􀕛   1 =\u003Cbr>8 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 2\u003Cbr>Q3: P(3 or less) ?\u003Cbr> 3 􀕍􀕞􀕍􀕖􀕜􀕛   3 =\u003Cbr>8 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 8 | Spinners\u003Cbr>| A spinner pictured at right, on bottom, has 8 equal sections. What are the following probabilities ?\u003Cbr>Q1: P(Number 2) ?\u003Cbr> 3 􀕍􀕞􀕍􀕖􀕜􀕛   3 =\u003Cbr>8 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 8\u003Cbr>Q2: P(Odd Number) ?\u003Cbr> 2+3 􀕍􀕞􀕍􀕖􀕜􀕛   5 \u003Cbr>=\u003Cbr>8 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 8\u003Cbr>Q3: P(3 or more) ?\u003Cbr> 3 􀕍􀕞􀕍􀕖􀕜􀕛   3 =\u003Cbr>8 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 8 |\n| --- | --- | --- |\n\nThrowing dice are commonly used to simulate random events. The nice thing about 6 sided dice is that they can be used for 2,3 or 6 different outcomes by grouping the results onto pairs or triplets. Also, the math of throwing two or more dice and adding the sums simulates new distributions of compound events.  \n\n| Dice\u003Cbr>Sample Space:\u003Cbr>All possible Events adding 2 Dice\u003Cbr>Sum 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 | A pair of standard dice are tossed. What are the following probabilities ? |  |  |\n| --- | --- | --- | --- |\n|  | Q1: P(Seven) ?\u003Cbr> 6 􀕍􀕞􀕍􀕖􀕜􀕛  36 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛\u003Cbr>Q2: P(Even Sum ) ? | = | 1\u003Cbr>6 |\n|  |  18 􀕍􀕞􀕍􀕖􀕜􀕛   1 =\u003Cbr>36 􀕘􀕗􀕛􀕛􀕑􀕊􀕔􀕍 􀕍􀕞􀕍􀕖􀕜􀕛 2\u003Cbr>Q3: P(Sum 9","cbCaiifsjWosnlHH","https://ap.wps.com/l/cbCaiifsjWosnlHH","pdf",434805,13,"English","# Probability\n## Coins and binomial probability\n## Spinners\n## Dice and compound events\n## Standard deck of cards\n## SHSAT lesson classwork questions","[{\"question\":\"What is a sample space in probability, and why is it useful?\",\"answer\":\"A sample space lists all possible events/outcomes for a given experiment. It helps verify probabilities by enumerating the complete set of outcomes.\"},{\"question\":\"How do you find probabilities for four fair coin tosses?\",\"answer\":\"Model the outcomes using a full sample space and count favorable results. Then convert the count into a probability out of 16 total outcomes (for four coins).\"},{\"question\":\"How are probabilities handled for spinners and dice in this lesson?\",\"answer\":\"For a spinner, probabilities come from counting labeled equally likely sectors. For dice, probabilities use dice sample spaces and count combinations that satisfy the required sum condition.\"}]","Chang Learning SHSAT Lesson 25 - Probability of Events | PDF",33]