{"id":5013,"date":"2022-08-17T18:04:03","date_gmt":"2022-08-17T18:04:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5013"},"modified":"2022-08-17T18:04:34","modified_gmt":"2022-08-17T18:04:34","slug":"8a-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/8a-preview\/","title":{"raw":"8A Preview","rendered":"8A Preview"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to construct a probability model to describe\u00a0 simple chance experiments, calculate the probability of a particular event using\u00a0 probabilities given in a table, and begin to think critically about the number of\u00a0 \u201csuccesses\u201d that would occur if a chance experiment were repeated multiple times.\r\n\r\nA probability model includes all possible outcomes of a chance experiment and the\u00a0 probabilities associated with those outcomes.\r\n\r\nImagine a fair spinner with 3 equally-sized sections: 1 section is red, 1 section is blue,\u00a0 and 1 section is yellow. If we spin the spinner, all 3 outcomes are equally likely, so the\u00a0 probability of each outcome is one-third. The following table displays the probability\u00a0 model.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Outcome<\/td>\r\nProbability<\/td>\r\n<\/tr>\r\n
Red<\/td>\r\n1\r\n\r\n3<\/td>\r\n<\/tr>\r\n
Yellow<\/td>\r\n1\r\n\r\n3<\/td>\r\n<\/tr>\r\n
Blue<\/td>\r\n1\r\n\r\n3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nLet\u2019s consider another chance experiment: rolling a fair, 6-sided die.\r\n
\r\n

Question 1<\/h3>\r\nFill in the following table to create a probability model for the outcomes that may\u00a0 occur when you roll a fair, 6-sided die. Represent the probabilities using fractions.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Outcome<\/td>\r\nProbability<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nHint: Dice have 6 sides that are labeled with the numbers 1\u20136, and since the die is fair, each of these outcomes is equally likely.\r\n\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\nIf you roll a fair die, what is the probability that the die will land on a number that is\u00a0 less than or equal to 2? Write your answer as a simplified fraction.\r\n\r\nHint: Use the probability rules you learned in In-Class Activity 7.B. We can rephrase\u00a0 the question by asking, \u201cWhat is the probability that the die will land on 1 or 2?\u201d\r\n\r\n<\/div>\r\n
\r\n

Question 3<\/h3>\r\nIf you roll a fair die, what is the probability that the die will land on a number that is in\u00a0 the range [1, 6]? Note that the endpoints, 1 and 6, are included in the range.\r\n\r\nHint: This range includes all possible outcomes of rolling a 6-sided die. Now let\u2019s consider another chance experiment: flipping a fair coin.\r\n\r\n<\/div>\r\n
\r\n

Question 4<\/h3>\r\nFill in the following table to create a probability model for the outcomes that may\u00a0 occur when you flip a fair coin. Represent the probabilities using decimals.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
Outcome<\/td>\r\nProbability<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/tr>\r\n
<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nHint: There are two possible ways that a coin can land. Since the coin is \u201cfair,\u201d these two outcomes are equally likely.\r\n\r\n<\/div>\r\n
\r\n

Question 5<\/h3>\r\nIf you flip a coin 10 times, are you guaranteed to get exactly 5 heads?\r\n\r\nHint: Remember the Law of Large Numbers that you learned about in In-Class\u00a0 Activity 7.A.\r\n\r\n<\/div>\r\nLooking ahead\r\n\r\nSometimes we carry out a chance experiment multiple times and count the number of\u00a0 \u201csuccesses.\u201d To describe this scenario, we could use a probability distribution, which\u00a0 lists all possible values of a random variable and the probabilities associated with those\u00a0 values.\r\n
\r\n

Question 6<\/h3>\r\nSuppose we flip a coin twice. Complete the list of possible values below.\r\n
    \r\n \t
  • Tails on the first flip and heads on the second flip<\/li>\r\n \t
  • Heads on the first flip and tails on the second flip<\/li>\r\n \t
  • <\/li>\r\n \t
  • <\/li>\r\n<\/ul>\r\nHint: The list should include all possible combinations of heads and tails for the two flips.\r\n\r\n<\/div>\r\n
    \r\n

    Question 7<\/h3>\r\nFill in the following table to complete the probability distribution for the number of\u00a0 heads that would occur in 2 coin flips.\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Number\u00a0 of Heads<\/td>\r\nProbability<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n#\r\n\r\n$ = 0.25<\/td>\r\n<\/tr>\r\n
    1<\/td>\r\n<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nHint: There are 4 possible outcomes for a set of 2 coin flips, and only one of them\u00a0 results in 0 heads. That is why the probability of getting 0 heads is one-fourth.\r\n\r\n \r\n\r\n<\/div>\r\n \r\n\r\n ","rendered":"

    Preparing for the next class<\/p>\n

    In the next in-class activity, you will need to construct a probability model to describe\u00a0 simple chance experiments, calculate the probability of a particular event using\u00a0 probabilities given in a table, and begin to think critically about the number of\u00a0 \u201csuccesses\u201d that would occur if a chance experiment were repeated multiple times.<\/p>\n

    A probability model includes all possible outcomes of a chance experiment and the\u00a0 probabilities associated with those outcomes.<\/p>\n

    Imagine a fair spinner with 3 equally-sized sections: 1 section is red, 1 section is blue,\u00a0 and 1 section is yellow. If we spin the spinner, all 3 outcomes are equally likely, so the\u00a0 probability of each outcome is one-third. The following table displays the probability\u00a0 model.<\/p>\n

    \n\n\n\n\n\n\n
    Outcome<\/td>\nProbability<\/td>\n<\/tr>\n
    Red<\/td>\n1<\/p>\n

    3<\/td>\n<\/tr>\n

    Yellow<\/td>\n1<\/p>\n

    3<\/td>\n<\/tr>\n

    Blue<\/td>\n1<\/p>\n

    3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    Let\u2019s consider another chance experiment: rolling a fair, 6-sided die.<\/p>\n

    \n

    Question 1<\/h3>\n

    Fill in the following table to create a probability model for the outcomes that may\u00a0 occur when you roll a fair, 6-sided die. Represent the probabilities using fractions.<\/p>\n

    \n\n\n\n\n\n\n\n\n\n
    Outcome<\/td>\nProbability<\/td>\n<\/tr>\n
    <\/td>\n<\/td>\n<\/tr>\n
    <\/td>\n<\/td>\n<\/tr>\n
    <\/td>\n<\/td>\n<\/tr>\n
    <\/td>\n<\/td>\n<\/tr>\n
    <\/td>\n<\/td>\n<\/tr>\n
    <\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    Hint: Dice have 6 sides that are labeled with the numbers 1\u20136, and since the die is fair, each of these outcomes is equally likely.<\/p>\n<\/div>\n

    \n

    Question 2<\/h3>\n

    If you roll a fair die, what is the probability that the die will land on a number that is\u00a0 less than or equal to 2? Write your answer as a simplified fraction.<\/p>\n

    Hint: Use the probability rules you learned in In-Class Activity 7.B. We can rephrase\u00a0 the question by asking, \u201cWhat is the probability that the die will land on 1 or 2?\u201d<\/p>\n<\/div>\n

    \n

    Question 3<\/h3>\n

    If you roll a fair die, what is the probability that the die will land on a number that is in\u00a0 the range [1, 6]? Note that the endpoints, 1 and 6, are included in the range.<\/p>\n

    Hint: This range includes all possible outcomes of rolling a 6-sided die. Now let\u2019s consider another chance experiment: flipping a fair coin.<\/p>\n<\/div>\n

    \n

    Question 4<\/h3>\n

    Fill in the following table to create a probability model for the outcomes that may\u00a0 occur when you flip a fair coin. Represent the probabilities using decimals.<\/p>\n

    \n\n\n\n\n\n
    Outcome<\/td>\nProbability<\/td>\n<\/tr>\n
    <\/td>\n<\/td>\n<\/tr>\n
    <\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

    Hint: There are two possible ways that a coin can land. Since the coin is \u201cfair,\u201d these two outcomes are equally likely.<\/p>\n<\/div>\n

    \n

    Question 5<\/h3>\n

    If you flip a coin 10 times, are you guaranteed to get exactly 5 heads?<\/p>\n

    Hint: Remember the Law of Large Numbers that you learned about in In-Class\u00a0 Activity 7.A.<\/p>\n<\/div>\n

    Looking ahead<\/p>\n

    Sometimes we carry out a chance experiment multiple times and count the number of\u00a0 \u201csuccesses.\u201d To describe this scenario, we could use a probability distribution, which\u00a0 lists all possible values of a random variable and the probabilities associated with those\u00a0 values.<\/p>\n

    \n

    Question 6<\/h3>\n

    Suppose we flip a coin twice. Complete the list of possible values below.<\/p>\n

      \n
    • Tails on the first flip and heads on the second flip<\/li>\n
    • Heads on the first flip and tails on the second flip<\/li>\n
    • <\/li>\n
    • <\/li>\n<\/ul>\n

      Hint: The list should include all possible combinations of heads and tails for the two flips.<\/p>\n<\/div>\n

      \n

      Question 7<\/h3>\n

      Fill in the following table to complete the probability distribution for the number of\u00a0 heads that would occur in 2 coin flips.<\/p>\n

      \n\n\n\n\n\n\n
      Number\u00a0 of Heads<\/td>\nProbability<\/td>\n<\/tr>\n
      0<\/td>\n#<\/p>\n

      $ = 0.25<\/td>\n<\/tr>\n

      1<\/td>\n<\/td>\n<\/tr>\n
      2<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

      Hint: There are 4 possible outcomes for a set of 2 coin flips, and only one of them\u00a0 results in 0 heads. That is why the probability of getting 0 heads is one-fourth.<\/p>\n

       <\/p>\n<\/div>\n

       <\/p>\n

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