Probablity and statistics Question Need URGENT The probability

vadulgattp

vadulgattp

Answered question

2021-11-13

Probablity and statistics Question
Need URGENT
The probability that an automobile being filled with gasoline will also need an oil change is 0.37; the probability that it needs a new oil filter is 0.45; and the probability that both the oil and filter need changing is 0.20.
(a) If the oil had 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

Alicia Washington

Alicia Washington

Beginner2021-11-14Added 23 answers

Step 1
(a)The probability that a new oil filter is needed, if oil has to be changed is obtained below:
Define event C as automobile being filled with gasoline and needs an oil change, event O as automobile needs oil filter.
The corresponding probabilities are,
P(C)=0.37
P(CO)=0.20
The required probability is,
P(OC)=P(CO)P(C)
=0.200.37=0.5405
Part a
The probability of a new oil filter is needed; if oil has to be changed is 0.5405.
Explanation | Common mistakes | Hint for next step
The conditional probability of O∣C is, to obtain probability of event O when event ‘C’ has already occurred. This is done by taking the ratio of probability of intersection of two events O and C and probability event C. It can be expected that about 54% of times the automobile needs new oil filter; if oil has to be changed.
Step 2
(b) The probability oil has to be changed, if that a new oil filter is needed is obtained below:
The corresponding probabilities are,
P(O)=0.45
P(CO)=0.20
The required probability is,
P(CO)=P(CO)P(C)
=0.200.45=0.444
Part b
The probability oil has to be changed, if that a new oil filter is needed is 0.444.
Explanation | Common mistakes
The conditional probability of C∣O is, to obtain probability of event C when event ‘O’ has already occurred. This is done by taking the ratio of probability of intersection of two events O and C and probability event O. It can be expected that about 44% of times the oil has to be changed, if automobile needs new filter.
Answer:
Part a
The probability of a new oil filter is needed; if oil has to be changed is 0.5405.
Part b
The probability oil has to be changed, if that a new oil filter is needed is 0.444.

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