Ask Question
MathematicsMathematics
2 December, 19:30

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?

+4
Answers (1)
  1. 2 December, 19:46
    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 the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers
You Might be Interested in
1. Jacob opens an online-only savings account and deposits $50 each month. The annual interest rate is 2.5 percent. Interest is compounded monthly. What is the total amount in the account after 5 months?
Answers (1)
So, in Math I am learning Scientific Notation. Can someone show an example and some tips for me as well as the steps to remember how to turn things into and out of the Scientific Notation form? Thanx a bunch!
Answers (1)
Damita wants to read a 257 page book in one week. She plans to read 36 pages each day. Will she reach her goal? Explain
Answers (1)
The area of a rectangular room is 120 square feet. The width is 10 feet. What is the length?
Answers (1)
A jet travels 3255 miles against a jetstream in 5 hours and 4055 miles with the jetstream in the same amount of time. What is the rate of the jet in still air and what is the rate of the jetstream?
Answers (1)
New Questions in Mathematics
A stories giving a $10 coupon to every 7th person that enters the store and a $25 coupon to every 18th person to enter the store. Which person will be the first to get both coupons
Answers (1)
in geometry, two lines are parallel if they are in the same plane and never intersect. Take the mathematical concept of parallel lines and apply it to non-mathematical situations or objects.
Answers (1)
When deciding to model a situation with 3D figures, what are the most important things to remember?
Answers (1)
Find g[h (x) ] and h[g (x) ] 2. g (x) = -3x h (x) = 4x - 1
Answers (1)
1. In what country did the government debate the merit of teaching students quadratics? 2. What modern technology would not be possible without quadratics? (hint: I have one at my house.) 3. What great ideas did the Babylonians come up with? 4.
Answers (1)
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?