Ask Question
MathematicsMathematics
4 February, 23:33

You toss three 6-sided dice and record the sum of the three faces facing up. a) Describe precisely a sample space S for this experiment. b) What is the probability that the sum is 16 or more? c) What is the probability the sum is exactly 4 or 5? d) What is the probability the sum is less than 17?

+5
Answers (1)
  1. 5 February, 02:22
    0
    a.) Sample space means all possible outcomes, since we know the dice are 6 face, then the sample space becomes all possible outcomes when we toss the die.

    b.) 9/216

    c.) 9/216

    d.) 212/216

    Step-by-step explanation:

    Sample space means all possible outcomes, since we know the dice are 6 face, then the sample space becomes all possible outcomes when we toss the die.

    [1,1,1] [1,1,2] [1,1,3] [1,1,4] [1,1,5] [1,1,6]

    [1,2,1] [1,2,2] [1,2,3] [1,2,4] [1,2,5] [1,2,6],

    [1,3,1] [1,3,2] [1,3,3] [1,3,4] [1,3,5] [1,3,6]

    [1,4,1] [1,4,2] [1,4,3] [1,4,4] [1,4,5] [1,4,6]

    [1,5,1] [1,5,2] [1,5,3] [1,5,4] [1,5,5] [1,5,6]

    [1,6,1] [1,6,2] [1,6,3] [1,6,4] [1,6,5] [1,6,6]

    [2,1,1] [2,1,2] [2,1,3] [2,1,4] [2,1,5] [2,1,6]

    [2,2,1] [2,2,2] [2,2,3] [2,2,4] [2,2,5] [2,2,6],

    [2,3,1] [2,3,2] [2,3,3] [2,3,4] [2,3,5] [2,3,6]

    [2,4,1] [2,4,2] [2,4,3] [2,4,4] [2,4,5] [2,4,6]

    [2,5,1] [2,5,2] [2,5,3] [2,5,4] [2,5,5] [2,5,6]

    [2,6,1] [2,6,2] [2,6,3] [2,6,4] [2,6,5] [2,6,6]

    [3,1,1] [3,1,2] [3,1,3] [3,1,4] [3,1,5] [3,1,6]

    [3,2,1] [3,2,2] [3,2,3] [3,2,4] [3,2,5] [3,2,6],

    [3,3,1] [3,3,2] [3,3,3] [3,3,4] [3,3,5] [3,3,6]

    [3,4,1] [3,4,2] [3,4,3] [3,4,4] [3,4,5] [3,4,6]

    [3,5,1] [3,5,2] [3,5,3] [3,5,4] [3,5,5] [3,5,6]

    [3,6,1] [3,6,2] [3,6,3] [3,6,4] [3,6,5] [3,6,6]

    [4,1,1] [4,1,2] [4,1,3] [4,1,4] [4,1,5] [4,1,6]

    [4,2,1] [4,2,2] [4,2,3] [4,2,4] [4,2,5] [4,2,6],

    [4,3,1] [4,3,2] [4,3,3] [4,3,4] [4,3,5] [4,3,6]

    [4,4,1] [4,4,2] [4,4,3] [4,4,4] [4,4,5] [4,4,6]

    [4,5,1] [4,5,2] [4,5,3] [4,5,4] [4,5,5] [4,5,6]

    [4,6,1] [4,6,2] [4,6,3] [4,6,4] [4,6,5] [4,6,6]

    [5,1,1] [5,1,2] [5,1,3] [5,1,4] [5,1,5] [5,1,6]

    [5,2,1] [5,2,2] [5,2,3] [5,2,4] [5,2,5] [5,2,6],

    [5,3,1] [5,3,2] [5,3,3] [5,3,4] [5,3,5] [5,3,6]

    [5,4,1] [5,4,2] [5,4,3] [5,4,4] [5,4,5] [5,4,6]

    [5,5,1] [5,5,2] [5,5,3] [5,5,4] [5,5,5] [5,5,6]

    [5,6,1] [5,6,2] [5,6,3] [5,6,4] [5,6,5] [5,6,6]

    [6,1,1] [6,1,2] [6,1,3] [6,1,4] [6,1,5] [6,1,6]

    [6,2,1] [6,2,2] [6,2,3] [6,2,4] [6,2,5] [6,2,6],

    [6,3,1] [6,3,2] [6,3,3] [6,3,4] [6,3,5] [6,3,6]

    [6,4,1] [6,4,2] [6,4,3] [6,4,4] [6,4,5] [6,4,6]

    [6,5,1] [6,5,2] [6,5,3] [6,5,4] [6,5,5] [6,5,6]

    [6,6,1] [6,6,2] [6,6,3] [6,6,4] [6,6,5] [6,6,6]

    b.) Probability that the sum is 16 or more is

    Pr[4,6,6] + pr[5,5,6] + pr [ 5,6,5] + pr [5,6,6] + pr [6,5,5] + pr [6,5,6] + pr [6,6,4] + pr[6,6,5] + pr [6,6,6]

    Becomes:

    [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ = 9/216

    Probability that the sum is 4 or 5 is

    Pr [ 1,1,2] or pr[1,2,2] or pr [1,1,3] or pr [1,2,1] or pr[2,1,2] or pr[1,3,1] or pr[3,1,1] or pr[2,1,1] or pr[2,2,1]

    Becomes:

    [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ = 9/216

    Probability that the sum is less than 17

    We take it as:

    1 - probability that the sum is 17 and above.

    Now probability that the sum is 17 and above becomes

    pr[5,6,6] or pr[6,5,6] or pr[6,6,5] or pr[6,6,6]

    = [1/6]³ + [1/6]³ + [1/6]³ + [1/6]³ = 4/216

    Hence, probability that the sum is less than 17 becomes:

    1-4/216 = 212/216.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “You toss three 6-sided dice and record the sum of the three faces facing up. a) Describe precisely a sample space S for this experiment. b) ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers
You Might be Interested in
An event has a theoretical probability of 0.5. what does this mean?
Answers (1)
Each baseball team has nine players and each football team has eleven players. Six schools have both baseball and football teams. Four schools have only a baseball team. How many players are there for all ten schools?
Answers (2)
What is the ratio for the volumes of two similar spheres, given that the ratio of their radii is 3:4?
Answers (2)
Rosa works in an office building with many floors. From her office, she goes down 2 floors for a meeting. Then, she goes up 8 floors to have lunch. After lunch, she goes down 13 floors to the first floor. What floor is Rosa's office on?
Answers (1)
170 percent converted to a fraction equals: ... ?
Answers (2)
New Questions in Mathematics
Which function describes the arithmetic sequence shown? 1, - 2, - 5, - 8, - 11, ... A) ƒ (x) = 3x + 4 B) ƒ (x) = 3x - 4 C) ƒ (x) = - 3x + 4 D) ƒ (x) = - 3x - 4
Answers (1)
What is the quotient of - 27 and 5
Answers (1)
A rectangle in Quadrant I rotates 270° counterclockwise. In which quadrant will the transformation lie?
Answers (2)
Hera spent $16 on dinner. Then she spent $6 on dessert and some more on a taxi ride. Including the taxi fare, she spent a total of $31.
Answers (1)
How do you write 2.2 in word form?
Answers (2)
Home » Mathematics » You toss three 6-sided dice and record the sum of the three faces facing up. a) Describe precisely a sample space S for this experiment.
Sign Up Forgot Password?