Question

If you’re good with probability math 30 please help with questions 33 and 35! real answers only

Answer 1

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

$P(D'\cap F) = \dfrac{6+21}{13+6+21+3+5+8+15+11}\quad =\large\boxed{\dfrac{27}{82}}$

34)

Red  = 26

Face  = 12

Red ∩ Face = 6

Total cards = 52

R ∪ F = R + F - (R ∩ F)

        = 26 + 12 - 6

        = 32

$P(R\cup F)=\dfrac{R\cup F}{Total}\quad =\dfrac{32}{52}\quad \rightarrow \quad \large\boxed{\dfrac{8}{13}}$

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".

$P(C) = \dfrac{34+17+3+9}{Total} =\dfrac{53}{80}\quad \bigg(not\ \dfrac{34}{75}\bigg)\qquad \text{This is False.}\\\\\\P(S\cap T)=\dfrac{9+0}{Total}=\dfrac{9}{80}\quad \bigg(not\ \dfrac{12}{75}\bigg)\qquad \text{This is False.}\\\\\\\\P(C\cup T)\cup S = \dfrac{17+9+3+4}{Total}= \dfrac{33}{80}\quad \bigg(not\ \dfrac{38}{75}\bigg)\qquad \text{This is False.}\\\\\\P(C\cup T)\cap S'=\dfrac{34+17+8}{Total}=\dfrac{59}{80}\quad \bigg(not\ \dfrac{59}{75}\bigg)\quad \text{This is False.}$