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A fair dice has six faces numbered 1, 1, 1, 2, 3, & 4.
The dice is rolled twice and the number is shown recorded each time.
Find the probability that the sum of the two numbers recorded is at least 4.

 Apr 11, 2020
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There are 6*6=36 possible rolls, and while some of these are the same they need to be counted multiple times because they have a higher chance of occuring.

Rolls that sum to 4, with frequency:

(1,3) x3

(3,1) x3

(2,2) x1

 

Sum to 5:

(1,4) x3

(4,1) x3

(3,2) x1

(2,3) x1

 

Sum to 6:

(3,3) x1

(2,4) x1

(4,2) x1

 

Sum to 7:

(3,4) x1

(4,3) x1

 

8:

(4,4) x1

 

Adding up the frequencies gets 21

The probability is 21/36=7/12

 Apr 11, 2020

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