Question

Medal
Two six-sided dice are rolled. Find the probability of the given outcome (express your answers as fractions in lowest terms).
(a) The sum of the dots on the upward faces is 8.


(b) The sum of the dots on the upward faces is greater than 4.

Answer 1

first lets make the sample space for rolling two die.
The notation I am using is (first die, second die)
$$ \Large {
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\\
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\\
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)\\
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)\\
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\\
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6) \\
}$$

Answer 2

okay

Answer 3

so where would we start

Answer 4

now we want the sum of the two dice, so you can add each of these

Answer 5

so 1+1 ,1+2 like that

Answer 6

ok whats the next step

Answer 7

we want probability of getting a sum of 8

Answer 8

so we find numbers which equal 8?

Answer 9

$$ \Large {
2~~3~~4~~5~~6~~7 \\
3~~4~~5~~6~~7~~\color{red}{8} \\
4~~5~~6~~7~~\color{red}{8}~~9\\
5~~6~~7~~\color{red}8~~9~10 \\
6~~7~~\color{red}8~~9~10~11 \\
7~~\color{red}8~~9~10~11~12\\

}$$

Answer 10

5/8

Answer 11

there are 36 sample points

Answer 12

5/36

Answer 13

m i right?

Answer 14

yes

Answer 15

is that the answer for part a?

Answer 16

yes

Answer 17

ok how would we do part b

Answer 18

30/36

Answer 19

$$

\Large{


\begin{array}{c|cccc}
\text{+} &1 & 2 & 3 & 4 & 5 & 6 \\
\hline
1 & 2 & 3 & 4&5 & 6& 7 \\
2 & 3 & 4&5 & 6&7&8 \\
3 & 4&5 &6 & 7 & 8 &9\\
4&5 &6 & 7 & 8 &9&10\\
5 &6 & 7 & 8 &9&10&11\\
6 & 7 & 8 &9&10&11&12\\


\end{array}




}
$$

Answer 20

so how would you figure this out

Answer 21

so we want greater than 4

Answer 22

yes

Answer 23

21/36

Answer 24

$$
\Large{
\begin{array}{c|cccc}
\text{+} &1 & 2 & 3 & 4 & 5 & 6 \\
\hline
1 & 2 & 3 & 4 &\color{red}5 & \color{red}6& \color{red}7 \\
2 & 3 & 4& \color{red}5 & \color{red}6&\color{red}7&\color{red}8 \\
3 & 4&\color{red}5 &\color{red}6 &\color{red}7 & \color{red}8 &\color{red}9\\
4&\color{red}5&\color{red}6&\color{red}7 & \color{red}8 &\color{red}9&\color{red}{10}\\
5 &\color{red}6 & \color{red}7 & \color{red}8 &\color{red}9&\color{red}{10}&\color{red}{11}\\
6 & \color{red}7 & \color{red}8 &\color{red}9& \color{red}{10}&\color{red}{11}&\color{red}{12}\\


\end{array}


}
$$

Answer 25

we want all sample points greater than 4.
there should be 30 sample points
note that there are 6 which are four or less

Answer 26

30/36

Answer 27

5/6

Answer 28

right

Answer 29

so the answer is 5/6

Answer 30

yes

Answer 31

thank you