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Rolling Dice When 2 dice are rolled, find the probability
Chapter 4, Problem 26CQ(choose chapter or problem)
Problem 26CQ
Rolling Dice When 2 dice are rolled, find the probability of gening
a. A sum of 6 or 7
b. A sum greater than 8
c. A sum less than 3 or greater than 8
d. A sum that is divisible by 3
e. A sum of 16
f. A sum less than 11
Questions & Answers
QUESTION:
Problem 26CQ
Rolling Dice When 2 dice are rolled, find the probability of gening
a. A sum of 6 or 7
b. A sum greater than 8
c. A sum less than 3 or greater than 8
d. A sum that is divisible by 3
e. A sum of 16
f. A sum less than 11
ANSWER:
Solution 26CQ
Step1 of 7:
From the given problem we have two fair dice. We know that a fair die has 6 faces that is
{1, 2, 3, 4, 5, 6}. Then, the total number of outcomes is = 36.
Here our goal is:
a). We need to find the probability of a sum of 6 or 7.
b). We need to find the probability of a sum greater than 8.
c). We need to find the probability of a sum less than 3 or greater than 8.
d). We need to find the probability of a sum that is divisible by 3.
e). We need to find the probability of a sum of 16.
f). We need to find the probability of a sum less than 11.
The possible number of outcomes are:
{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (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)}
Step2 of 7:
a).
The possible number of outcomes that have sum 6 is:
{(1,5), (2,4), (3,3), (4,2), (5,1)}
Similarly, The possible number of outcomes that have sum 7 is:
Then, The probability of a sum of 6 or 7 is:
Therefore, The probability of a sum of 6 or 7 is 0.3054.