SOLUTION: 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

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
:
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
:

RELATED QUESTIONS
Two dice are rolled. The score on the dice is no more than 7. Find the probability (answered by math_helper)

two dice are rolled. Find the probability that the score on the dice is either 7 or... (answered by stanbon)

two dice are rolled. Find the odds that the score on the dice is... (answered by ikleyn)

two dice are rolled. find the probablility that the score on the dice is either 12 or at... (answered by Edwin McCravy)

Two dice are rolled simultaneously the score is the sum of numbers the dice land on. Find (answered by Boreal)

Two dice are rolled. Which is the probability that the score on the dice is either 12 or... (answered by edjones)

Two dice are rolled. Find the odds that the score on the dice is either 8 or at most 5. (answered by math_helper)

Two standard dice are rolled. What is the probability of the sum on the two dice being... (answered by stanbon)

Two standard dice are rolled. What is the probability of the sum on the two dice being... (answered by ilana)