Answer: 33) b 34) a 35) none
Step-by-step explanation:
33)
Filling in the Venn Diagram (from Left to right, including outside of circles):
T only = 13
(T ∩ F)only = 6
F only = 21
(T ∩ D) only = 3
T ∩ F ∩ D = 5
(F ∩ D) only = 8
D only = 15
(T ∪ F ∪ D)' = 11
TOTAL = 82
[tex]P(D'\cap F) = \dfrac{6+21}{13+6+21+3+5+8+15+11}\quad =\large\boxed{\dfrac{27}{82}}[/tex]
34)
Red = 26
Face = 12
Red ∩ Face = 6
Total cards = 52
R ∪ F = R + F - (R ∩ F)
= 26 + 12 - 6
= 32
[tex]P(R\cup F)=\dfrac{R\cup F}{Total}\quad =\dfrac{32}{52}\quad \rightarrow \quad \large\boxed{\dfrac{8}{13}}[/tex]
35) Note that the total is 34 + 17 + 8 + 3 + 9 + 4 + 5 = 80
I think the teacher made an error, if so, then the answer is "d".
[tex]P(C) = \dfrac{34+17+3+9}{Total} =\dfrac{53}{80}\quad \bigg(not\ \dfrac{34}{75}\bigg)\qquad \text{This is False.}\\\\\\P(S\cap T)=\dfrac{9+0}{Total}=\dfrac{9}{80}\quad \bigg(not\ \dfrac{12}{75}\bigg)\qquad \text{This is False.}\\\\\\\\P(C\cup T)\cup S = \dfrac{17+9+3+4}{Total}= \dfrac{33}{80}\quad \bigg(not\ \dfrac{38}{75}\bigg)\qquad \text{This is False.}\\\\\\P(C\cup T)\cap S'=\dfrac{34+17+8}{Total}=\dfrac{59}{80}\quad \bigg(not\ \dfrac{59}{75}\bigg)\quad \text{This is False.}[/tex]
