Math(Probability)

posted by .

Let X and Y equal the outcomes when two fair six-sided dice are rolled. Let
W = X + Y. Assuming independence, find the p.m.f. of W when
(a) The first die has three faces numbered 0 and three faces numbered 2, and the second die has its faces numbered 0, 1, 4, 5, 8, and 9.
(b) The faces on the first die are numbered 0, 1, 2, 3, 4, and 5, and the faces on the second die are numbered 0, 6, 12, 18, 24, and 30.

  • Math(Probability) -

    Outcomes of the first die:
    {0,0,0,2,2,2}
    Outcomes of the second die:
    {0,1,4,5,8,9}
    There are 36 outcomes for W=x+y, some of which are identical. Make a table and compile the sums:
    X 0 0 0 2 2 2
    0 0 0 0 2 2 2
    1 1 1 1 3 3 3
    4 4 4 4 6 6 6
    5 5 5 5 7 7 7
    8 8 8 8 10 10 10
    9 9 9 9 11 11 11

    Now compile the count of the outcomes, and divide by 36 to get the pmf (probability mass function)
    0 3 1/12
    1 3 1/12
    2 3 1/12
    3 3 1/12
    4 3 1/12
    5 3 1/12
    6 3 1/12
    7 3 1/12
    8 3 1/12
    9 3 1/12
    10 3 1/12
    11 3 1/12

    Part b is similar to part a.
    Post your answer for a check if you wish.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Two dice are rolled. Find the probability that a multiple of three is rolled on one die and an even number is rolled on the second die.
  2. math

    A six sided die is rolled three times. List possible outcomes and find the probability of rolling exactly one 6.
  3. probability

    Two six-sided dice each have the numbers 1 through 6 on their faces. Neither die is fair, but they are both weighted the same. The probability of rolling a certain number on one die is given in the table below: # 1 2 3 4 5 6 probability …
  4. Geometry

    Six standard six-sided die are rolled. Let p be the probability that the dice can be arranged in a row such that for 1\leq k \leq 6 the sum of the first k dice is not a multiple of 3. Then p can be expressed as \frac{a}{b} where a …
  5. math

    A fair six sided dice has the faces numbered from 1 to 6. The dice is thrown 4 time. Calculate the probability of exactly 2 fives. the answer is 25/216
  6. probability

    We have two fair three-sided dice, indexed by i=1,2. Each die has sides labelled 1, 2, and 3. We roll the two dice independently, one roll for each die. For i=1,2, let the random variable Xi represent the result of the ith die, so …
  7. Probability

    When two fair six-sided dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the two dice is 8.
  8. math

    A specially made pair of dice has only one- and two-spots on the faces. One of the dice has three faces with one-spot and three faces with two-spot. The other die has two faces with one-spot and four faces with a two-spot. One of the …
  9. math

    A specially made pair of dice has only one- and two-spots on the faces. One of the dice has three faces with one-spot and three faces with two-spot. The other die has two faces with one-spot and four faces with a two-spot. One of the …
  10. Math

    A fair eight-sided die is rolled six times. A success is getting a 6, 7 and 8. Find the probability of getting three successes.

More Similar Questions