The probability that an automobile being filled with gasoline also nee

gainejavima

gainejavima

Answered question

2021-11-18

The probability that an automobile being filled with gasoline also needs an oil change is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and the filter need changing is 0.14.
(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?

Answer & Explanation

Crom1970

Crom1970

Beginner2021-11-19Added 6 answers

Step 1
It is given that the probability that both the oil and the filter need changing is 0.14, the probability that an automobile being filled with gasoline also needs an oil change is 0.25 and the probability that it needs a new oil filter is 0.40.
Step 2
a) The probability that a new oil filter is needed if the oil has to be changed is obtained as follows:
P(New oil filter is needed| Oil has to be changed)=P(Both the oil and the filter need changing)P(Oil has to be changed)
=0.140.25
=0.56
b) The probability that oil has to be changed if a new oil filter is needed is obtained as follows:
P(Oil has to be changed | New oil filter is needed)=P(Both the oil and the filter need changing)P(New oil filter is needed)
=0.140.40
=0.35

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