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

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) = (6+21)/(13+6+21+3+5+8+15+11)\quad =\large\boxed{(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)=(R\cup F)/(Total)\quad =(32)/(52)\quad \rightarrow \quad \large\boxed{(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) = (34+17+3+9)/(Total) =(53)/(80)\quad \bigg(not\ (34)/(75)\bigg)\qquad \text{This is False.}\\\\\\P(S\cap T)=(9+0)/(Total)=(9)/(80)\quad \bigg(not\ (12)/(75)\bigg)\qquad \text{This is False.}\\\\\\\\P(C\cup T)\cup S = (17+9+3+4)/(Total)= (33)/(80)\quad \bigg(not\ (38)/(75)\bigg)\qquad \text{This is False.}\\\\\\P(C\cup T)\cap S'=(34+17+8)/(Total)=(59)/(80)\quad \bigg(not\ (59)/(75)\bigg)\quad \text{This is False.}`