4. in a large community, 72% of the people are adults, 78% of the people have traveled outside the state, and 11% are adults who have not traveled outside the state.
a. using a venn diagram or a hypothetical 1000 table, calculate the probability that a randomly selected person from the community is an adult and has traveled outside the state.
b. use the multiplication rule for independent events to decide whether the events "is an adult" and "has traveled outside the state" are independent.

a. The Venn diagram is explained in the attached word file.

0.61                                    

b. Not independent

Step-by-step explanation:

a. The hypothetical 1000 table for given situation is

                                          Adult(A)        Not Adult (not A)        Total

Travel outside (T)                 610                170                               780

Not Travel outside (not T)110                110                               220

Total                                 720                280                               1000

P(Adult and travel outside)=P(A and T)=610/1000=0.61

b. Multiplication rule for independent events is

P(A and B)=P(A)*P(B)

P(A and T)=0.61

P(A)*P(T)=0.72*0.78=0.56

As P(A and T) is not equal to P(A)*P(T), so event "being an adult" and "travel outside" are not independent.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)