Math Test 4: Probability Quiz
36 Questions
105 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which of the numbers that follow could represent a probability? I. 17/15 II. 0.1

  • only I
  • neither
  • both I and II
  • only II (correct)

    • Which of the numbers that follow could represent a probability? I. 50% II. 35%

  • only II
  • neither
  • both I and II (correct)
  • only I

    • If a die is rolled one time, find the probability of getting a number greater than 6.

  • 5/6
  • 0 (correct)
  • 1
  • 1/6

    • If a die is rolled one time, find the probability of getting a number less than 4 or an even number.

    <p>5/6</p> Signup and view all the answers

    A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is not blue?

    <p>11/16</p> Signup and view all the answers

    In a classroom, the students are 14 boys and 4 girls. If one student is selected at random, find the probability that the student is a girl.

    <p>2/9</p> Signup and view all the answers

    Of the next 33 trials on the docket in a county court, 4 are homicides, 11 are drug offenses, 7 are assaults, and 11 are property crimes. If jurors are assigned to trials randomly, what's the probability that a given juror won't get a property crime case?

    <p>2/3</p> Signup and view all the answers

    Evaluate 8!

    <p>40,320</p> Signup and view all the answers

    Evaluate the expression (4!)(3!)

    <p>144</p> Signup and view all the answers

    Evaluate the expression 8!/4!2!

    <p>840</p> Signup and view all the answers

    How many different ways can 3 people stand in line at a cash register?

    <p>6</p> Signup and view all the answers

    Evaluate 10P4.

    <p>5,040</p> Signup and view all the answers

    A. In how many ways can the letters in the word TEXAS be arranged? b. In how many ways can the letters in the word OHIO be arranged?

    <p>a. 120 b. 12</p> Signup and view all the answers

    Decide whether the selection described is a combination or a permutation. Five club members are chosen to serve on a committee.

    <p>combination</p> Signup and view all the answers

    Decide whether the selection described is a combination or a permutation. Three prizes are given to the winners of a race.

    <p>permutation</p> Signup and view all the answers

    Find both the number of combinations and the number of permutations for the given number of objects. 10 objects taken 7 at a time.

    <p>10C7 = 120; 10P7 = 604,800</p> Signup and view all the answers

    How many ways can a committee of 3 people be selected from a group of 8 people?

    <p>56</p> Signup and view all the answers

    How many different ways can a college select three applicants for a teaching position from a pool of 20 applicants?

    <p>1,140</p> Signup and view all the answers

    A teacher has 20 boys and 10 girls in her class. In how many ways can she select 6 of the children to be in a play if she must select 3 boys and 3 girls?

    <p>136,800</p> Signup and view all the answers

    How many ways can a person select four books, two CDs, and one DVD from ten books, twenty CDs, and five DVDs?

    <p>199,500</p> Signup and view all the answers

    Draw a tree diagram to determine the sample space when three coins are tossed.

    Signup and view all the answers

    Three coins are tossed. Find the probability that exactly two coins land tails up.

    <p>3/8</p> Signup and view all the answers

    Three coins are tossed. Find the probability that all the coins land heads up.

    <p>1/8</p> Signup and view all the answers

    Three coins are tossed. Find the probability that two or more coins land heads up.

    <p>1/2</p> Signup and view all the answers

    Three coins are tossed. Find the probability that no more than one coin lands heads up.

    <p>1/2</p> Signup and view all the answers

    A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 4 of diamonds.

    <p>1/52</p> Signup and view all the answers

    A single card is drawn from an ordinary 52-card deck. Find the probability of getting a black card.

    <p>1/2</p> Signup and view all the answers

    A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 7.

    <p>1/13</p> Signup and view all the answers

    A single card is drawn from an ordinary 52-card deck. Find the probability of getting a red 6.

    <p>1/26</p> Signup and view all the answers

    A single card is drawn from an ordinary 52-card deck. Find the probability of getting a diamond or a 10.

    <p>4/13</p> Signup and view all the answers

    A single card is drawn from an ordinary 52-card deck. Find the probability of getting a diamond and an ace.

    <p>1/52</p> Signup and view all the answers

    Two dice are rolled. Find the probability of getting a sum greater than 8.

    <p>5/18</p> Signup and view all the answers

    Two dice are rolled. Find the probability of getting a 5 on one die or on both dice.

    <p>11/36</p> Signup and view all the answers

    A package contains 14 candy canes, 8 of which are cracked. If 3 are selected, find the probability of getting no cracked candy canes.

    <p>0.0549</p> Signup and view all the answers

    A package contains 15 candy canes, 13 of which are cracked. If 2 are selected, find the probability of getting exactly one cracked candy cane.

    <p>0.2476</p> Signup and view all the answers

    To win a prize, a person must select 4 numbers from 15 numbers without replacement. Find the probability of winning if a person buys one ticket. (Note: The numbers can be selected in any order.) Round to four decimal places, if necessary.

    <p>0.0007</p> Signup and view all the answers

    Study Notes

    Probability Representation

    • Probabilities are values between 0 and 1, inclusive. Only the number 0.1 (II) represents a valid probability as 17/15 exceeds 1.

    Basic Probability of Die Rolls

    • The probability of rolling a number greater than 6 with a single die is 0, as a standard die has numbers only up to 6.
    • The probability of rolling a number less than 4 or an even number on a die is 5/6, including outcomes like 1, 2, 3, 4, and 6.

    Marbles and Probability

    • In a box with five blue, eight green, and three yellow marbles, the chance of selecting a marble that is not blue is 11/16.

    Classroom Gender Probability

    • A classroom with 14 boys and 4 girls gives a probability of 2/9 for randomly selecting a girl.

    Trials Probability

    • In a court with 33 trials, the probability a juror does not get a property crime case is 2/3, accounting for 26 other cases.

    Factorial Evaluation

    • 8! evaluates to 40,320, representing all possible arrangements of 8 distinct items.

    Permutations and Combinations

    • To calculate arrangements: (4!)(3!) = 144.
    • The expression 8!/4!2! evaluates to 840, representing combinations of groups.
    • For 10 objects taken 7 at a time: combinations (10C7) = 120, permutations (10P7) = 604,800.

    Committee Selection

    • Choosing 3 from 8 people gives 56 combinations.
    • Selecting 3 teachers from 20 applicants results in 1,140 arrangements.
    • A selection of 6 children (3 boys and 3 girls) from 20 totals 136,800 ways.

    Book, CD, DVD Selection

    • Selecting 4 books, 2 CDs, and 1 DVD among 10 books, 20 CDs, and 5 DVDs results in 199,500 possibilities.

    Coin Toss Probability

    • Tossing three coins, the probability of getting exactly two tails up is 3/8.
    • The probability that all coins show heads is 1/8; two or more heads appear with a probability of 1/2; no more than one head appears with a probability of 3/8.

    Card Drawing Probabilities

    • Drawing a 4 of diamonds from a 52-card deck has a probability of 1/52.
    • The chance of picking a black card is 1/2, and for a 7, it's 1/13.
    • The probability of drawing a red 6 is 1/26; for drawing a diamond or 10, it's 4/13.
    • The probability of selecting a diamond and an ace simultaneously is also 1/52.

    Dice Rolling Probability

    • When rolling two dice, the probability of achieving a sum greater than 8 is 5/18.
    • The chance of rolling a 5 on one or both dice is 11/36.

    Candy Cane Selection

    • From a package of 14 candy canes (8 cracked), the probability of selecting 3 without cracked ones is 0.0549.
    • Choosing 2 candy canes from 15 (13 cracked) has a 0.2476 chance of getting exactly one cracked.

    Lottery Probability

    • If selecting 4 numbers from 15 without replacement, the probability of winning with one ticket is approximately 0.0007.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    Test your understanding of probability concepts with this Math Test 4 quiz. Each question challenges you to identify which numbers can represent probabilities and calculate probabilities from given scenarios. Perfect for reinforcing your math skills!

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser