Determine whether the events E and F are independent or dependent
1.) Determine whether the events E and F are independent or dependent.
Justify your answer.
(a)
E: A person attaining a position as a professor attaining a position as a professor.
F: The same person attaining a PhD attaining a PhD.
A. E and F are independent because attaining a position as a professor attaining a position as a professor has no effect on the probability of a person
attaining a PhD.
B. E and F are dependent because attaining a position as a professor has no effect on the probability of a person attaining a PhD.
C. E and F are independent because attaining a PhD has no effect on the probability of a person
attaining a position as a professor
D. E and F are dependent because attaining a PhD can affect the probability of a person
attaining a position as a professor.
(b)
E: A randomly selected person planting tulip bulbs in October.
F: A different randomly selected person planting tulip bulbs in April.
A. E cannot affect F because “person 1
planting tulip bulbs in Octoberplanting tulip bulbs in October”
could never occur, so the events are neither dependent nor independent.
B. E can affect the probability of F, even if the two people are randomly selected, so the events are dependent.
C. E cannot affect F and vice versa because the people were randomly selected, so the events are independent.
D. E can affect the probability of F because the people were randomly selected, so the events are dependent.
(c)
E: The war in a major oil dash exporting country war in a major oil-exporting country.
F: The price of gasoline price of gasoline.
A.
The war in a major oil-exporting country war in a major oil-exporting country could affect the
price of gasoline, so E and F are dependent.
B.
The war in a major oil-exporting country could not affect the price of gasoline price of gasoline, so E and F are independent.
C.
The price of gasoline could affect the war in a major oil-exporting country war, so E and F are dependent.
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