Answer :
Answer:
See the below work.
Step-by-step explanation:
To find the outcomes of adding the scores when rolling two dice together, first we make the table of outcomes - refer to the 1st attached picture.
(a)
the total possible scores (outcome) = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
(b)
The results are not equally likely outcomes since the total numbers of each outcome are unequal:
[tex]\begin{array}{c|c}\cline{1-2}outcome&total\ (frequency)\\\cline{1-2}2&1\\3&2\\4&3\\5&4\\6&5\\7&6\\8&5\\9&4\\10&3\\11&2\\12&1\\\cline{1-2}\Sigma frequencey&36\\\cline{1-2}\end{array}[/tex]
(c)
We can find the probability by using the probability formula:
[tex]\boxed{P(A)=\frac{n(A)}{n(S)} }[/tex]
where:
- [tex]P(A)=\text{probability of event A}[/tex]
- [tex]n(A)=\text{number of outcome of event A}[/tex]
- [tex]n(S) = \text{total number of all outcomes}[/tex]
(i)
Given:
- [tex]n(x=10)=3[/tex]
- [tex]n(S)=36[/tex]
Then:
[tex]\begin{aligned} P(x=10)&=\frac{n(x=10)}{n(S)}\\\\&=\frac{3}{36} \\\\&=\bf\frac{1}{12} \end{aligned}[/tex]
(ii)
Given:
- [tex]n(x=1)=1[/tex]
- [tex]n(S)=36[/tex]
Then:
[tex]\begin{aligned} P(x=1)&=\frac{n(x=1)}{n(S)}\\\\&=\bf\frac{1}{36}\end{aligned}[/tex]
(iii)
Given:
- [tex]n(x=16)=0[/tex]
- [tex]n(S)=36[/tex]
Then:
[tex]\begin{aligned} P(x=16)&=\frac{n(x=16)}{n(S)}\\\\&=\frac{0}{36} \\\\&=\bf0 \end{aligned}[/tex]
(iv)
Given:
- [tex]n(x=12)=1[/tex]
- [tex]n(S)=36[/tex]
Then:
[tex]\begin{aligned} P(x=12)&=\frac{n(x=12)}{n(S)}\\\\&=\bf\frac{1}{36} \end{aligned}[/tex]
(v)
Given:
- [tex]n(x < 6)=1+2+3+4=10[/tex]
- [tex]n(S)=36[/tex]
Then:
[tex]\begin{aligned} P(x < 6)&=\frac{n(x < 6)}{n(S)}\\\\&=\frac{10}{36} \\\\&=\bf\frac{5}{18} \end{aligned}[/tex]
