Question 1152286: Two dice are rolled. Find the probability of the event described.
A) The score on the dice is no more than 7
B) The score on the dice is 7
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Consider the event space for rolling 2 dice
:
(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)
:
There are 6 * 6 = 36 events in the event space for rolling two dice
:
A) The events no more than 7 are (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2), (6,1)
:
There are 21 events that are no more than 7, therefore
:
Probability (P) (sum of dice is no more than 7) = 21/36 = 7/12
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B) The events where the sum is 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
:
There are 6 events that are equal to 7, therefore
:
P (sum of dice is 7) = 6/36 = 1/6
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