Question

In: Math

We roll two fair dice (a black die and a white die). Let x = the...

We roll two fair dice (a black die and a white die). Let
x = the number on the black die − the number on the white die,record x as the outcome of this random experiment.

(a) What is the probability space?

Expert Solution

I will try to explain it in very simple words:

Finding the probability space means finding each possible event and its probability.

Let's do this with regards to the specific question at hand:

X = ( 1 - 1 to 6) = (0,-1,-2,-3,-4,-5)

= (2 - 1 to 6) = (1,0,-1,-2,-3,-4)

= (3 - 1 to 6) = (2,1,0,-1,-2,-3)

= (4 - 1 to 6) = (3,2,1,0,-1,-2)

= (5 - 1 to 6) = (4,3,2,1,0,-1)

= (6 - 1 to 6) = (5,4,3,2,1,0)

X = (0,0,0,0,0,0,-1,-1,-1,-1,-1,-2,-2,-2,-2,-3,-3,-3,-4,-4,-5,1,1,1,1,1,2,2,2,2,3,3,3,4,4,5)

Probability of getting 0 = 6/36

Probability of getting - 1 = 5/36

Probability of getting - 2 = 4/36

Probability of getting - 3 = 3/36

Probability of getting - 4 = 2/36

Probability of getting - 5 = 1/36

Probability of getting 1 = 5/36

Probability of getting 2 = 4/36

Probability of getting 3 = 3/36

Probability of getting 4 = 2/36

Probability of getting 5 = 1/36

You may also assert that the sum of the probabilities of these events is equal to 1:

Sum = 6/36 + 5/36 + 4/36 + 3/36 + 2/36 + 1/36 + 5/36 + 4/36 + 3/36 + 2/36 + 1/36

= 1

Hope you understood, if you like this answer then a thumbs up would be really Appreciable.

milcah answered 1 month ago

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