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# Twonumber cubes are rolled.

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Twonumber cubes are rolled.

(a) List the sample space.

(b)What is the probability, as a simplified fraction, that the sum of the numbers is 4 or that the sum of the numbers is greater than 9? Show your work.

Mar 9, 2019

#1
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a) I'm assuming that you are rolling 2 6-sided dice:

Sample space = 6 x 6 = 36

b) Probability of rolling a sum of 4 is: 3+1, 1+3 and 2+2 =3/36 =1/12

Probability of rolling a sum > 9 is as follows: 6+4=10, 4+6=10 and 5+5=10, or: 3 / 36 =1/12

Probability of rolling a sum of 11 =6+5 and 5+6 =11, or: 2/36 = 1/18

Probability of rolling a sum of 12 = 6+6 = 12, or: 1 /36

So, the overall probability of rolling a sum > 9 is: 1/12 + 1/18 + 1/36 = 1/6

Mar 9, 2019
#2
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The sample space is not 36.  If we consider order of the dice as important then the size of the sample space is 36

but that is not the sample space.  The sample space consists of all pairs of numbers 1-6, i.e.

(1,1), (1,2) ... (1,6), (2,1), (2,2) ... (6,6)

Usually when rolling dice the order of dice is not considered important so it would be more accurate to describe the sample space

as all pairs of number 1-6 where the first number is greater than or equal to the second number (or vice versa).

In this case the size of the sample space is 6+(6*5)/2 = 21

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

Rom  Mar 9, 2019
#3
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http://www.math.hawaii.edu/~ramsey/Probability/TwoDice.html

Guest Mar 9, 2019