Question

6. Find the probability that the sum is 6 or that a double is rolled (doubles are 1 & 1, 2 & 2,3 & 3,

etc).
Use the following for problems 7 & 8. A single fair six-sided die is rolled.
7.
Find the probability that three rolls of the dice result in 5's.
8. Find the probability that the first roll results in a 2 and the second roll results in a 3.

Answer 1

Answer:
`\bold{(6)\ (5)/(18)\qquad (7)\ (1)/(216)\qquad (8)\ (1)/(36)}`

Explanation:

(6) Sum is 6 or doubles are rolled minus duplicates

(1,5) (2,4) (3,3) (4,2)(5,1) + (1,1)(2,2)(3,3)(4,4)(5,5)(6,6) - (3,3)

`(\# of\ outcomes)/(total\ possible\ outcomes)=(6)/(36)+(5)/(36)-(1)/(36)=(10)/(36)\rightarrow\large\boxed{(5)/(18)}`

(7) First roll and Second roll and Third roll

`(\# of\ outcomes)/(total\ possible\ outcomes)=(1)/(6)* (1)/(6)* (1)/(6)=\large\boxed{(1)/(216)}`

(8) First roll and Second roll

`(\# of\ outcomes)/(total\ possible\ outcomes)=(1)/(6)* (1)/(6)=\large\boxed{(1)/(36)}`