Mathematics

posted by .

When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below.

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Let X denote the absolute value of the difference of the two numbers. Find the probability distribution of X. Give the probabilities as decimals rounded to three decimal places.

• Mathematics -

For X=0, the two dice must roll equal values, such as (1,1),(2,2), ....

Count the number of such cases, divide it by 36 (number of possible outcomes) and assign the quotient to X(0).

Repeat the count for X(1) (i.e. difference =1, such as (3,2)...), X(2)....until X(5).
The sum of X(0)...X(5) should add up to 1.

• Mathematics -

Make a frequency distribution for the absolute differences of the values. The absolute difference probabilities will be the number of tosses with each difference divided by 36. For example, no difference ([1,1], [2,2,] etc.) would be 6/36 = 1/6 (convert to decimal). I5I (absolute difference) would be 2/36.

I'll let you do the rest.

The probabilities should sum as 1 (within rounding error) as a check.

I hope this helps.

• Mathematics -

456589

Similar Questions

1. precalculus

Suppose that wo dice, one red and one green are rolled. How Many different outcomes are possible for the pair of dice?
2. math

this is real hard and i would love some help. In a game of craps, a player rolls 2 balanced dice. There are 36 equally likely outcomes. What is the probability that: a) the sum is either 3 or 8 b) the sum is 6 or doubles rolled c) …
3. Math

When two balanced dice are rolled, 36 equally likely outcomes are possible. What are the odds of getting a 5 or 6?
4. Math

Suppose you play a game in which two fair standard dice are rolled. If the numbers showing on the dice are different, you lose \$2. If the numbers showing are the same, you win \$2 plus the dollar value of the sum of dice. Complete the …
5. Math

Three fair dice are rolled, and all outcomes are equally likely. What is the probability that the sum of all the numbers on the dice is at most 6?
6. Math

Three fair dice are rolled, and all outcomes are equally likely. What is the probability that the sum of all the numbers on the dice is at most 6?
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 115 Statistics

In the game of craps, the player rolls two balanced dice, 36 equally likely outcomes, compute the probability the player looses on the first roll if the sum of the dice is 3, 4, or 6.
9. Data management

Which of the following three events is more likely to happen that a person get a) At least 1 six when 6 dice are rolled; b) At least 2 sixes when 12 dice are rolled, or c) At least 3sixes when 18 dice are rolled. Explain why.
10. Math

A 10 sided dice numbered 1 to 10 rolled four times. a)Write how many outcomes will we get?

More Similar Questions