Question

3. The probability that an automobile being filled with gasoline also needs an oil change is 0.30; the probability that it needs a new oil filter is 0.72; and the probability that both the oil and the filter need changing is 0.18. (a) If the oil has to be changed, what is the probability that a new oil filter is needed? (b) If a new oil filter is needed, what is the probability that the oil has to be changed? 4. The probability a person has read a book in the past year is 0.72. The probability a person is considered a millennial is 0.30. The probability a person has read a book in the past year and is considered a millennial is 0.24. Are being considered a millennial and having read a book in the past year independent events? Explain.

3&4

Answer 1

3:

From the given information we have

P(oil changed) = 0.30, P(need new filter) = 0.72, P(oil changed and need new filter) = 0.18

(a)

P(need new filter | oil changed) = P(oil changed and need new filter) / P(oil changed) = 0.18 / 0.30 = 0.60

Answer: 0.60

(b)

P(oil changed | need new filter ) = P(oil changed and need new filter) / P(need new filter) = 0.18 / 0.72 = 0.25

Answer: 0.25

--------------------------------------------------

4:

P(read a book is past year) = 0.72, P(millennial) = 0.30, P(read a book is past year and millennial) = 0.24

Since

P(read a book is past year) *  P(millennial) = 0.72 *0.30 = 0.216

and it is not equal to P(read a book is past year and millennial)

so events "read a book is past year" and "millennial" are not independent.