Question

2A. What is the sample space of the following? Roll 2 four sided dice and record the sum.

2B. If you roll a six sided die and a 4 sided die, what is the probability that the sum will be 5?

Answer 1

solution:
A) Here, we are rolling the 2 four sided dice then the all possible outcome are as follows,
S={(1,1),(1,2),(1,3),(1,4),
(2,1,(2,2),(2,3),(2,4),
(3,1),(,3,2),(3,3),(3,4),
(4,1),(4,2),(4,3),(4,4)}
n(S)= 16
Let S1 be the sample space of sum of outcomes when the 2 four sided dice is rolled .
Then the possible sum of each outcome are as follows,
S1={2,3,4,5,6,7,8}
n(S1)=7
B) let S be the sample space of a rolling of a six dice and a 4 sided dice then the all possible outcome is,
S={(1,1),(1,2),(1,3),(1,4),
(2,1,(2,2),(2,3),(2,4),
(3,1),(,3,2),(3,3),(3,4),
(4,1),(4,2),(4,3),(4,4),
(5,1),(5,2),(5,3),(5,4),
(6,1)(6,2),(6,3),(6,4)}
n(S)= 24
Let A be the event that sum of the outcome is 5,
A={(1,4),(2,3),(3,2),(4,1)}
n(A)=4
By definition of the probability,
P(A)= n(A)/n(S)
= 4/24
=1/6
The probability that the sum will be 5 is 1/6