Problem

In a four-cylinder engine there are four spark plugs. If any one of them malfunctions, the...

In a four-cylinder engine there are four spark plugs. If any one of them malfunctions, the car will idle roughly and power will be lost. Suppose that for a certain brand of spark plugs the probability that a spark plug will function properly after 5,000 miles is .90. Assuming that the spark plugs operate independently, what is the probability that the car will idle roughly after 5,000 miles?

Step-by-Step Solution

Solution 1

From the information, observe that in a four-cylinder engine there are four spark plugs. If any one of them malfunctions, the car will idle roughly, and power will be lost.

Here, the probability that a spark plug will function properly after 5000 miles is 0.90

Calculate the probability that the car will idle roughly after 5000 miles.

$P[$ Car will idle after 500 miles $]=P[$ Atleast 1 spark plug malfunctions $]$ $=1-P[$ No spark plug malfunctions $]$ $=1-P[$ All 4 spark plugs function properly $]$

$$ \begin{aligned} &=1-(0.90)^{4} \\ =0.3439 & \end{aligned} $$

Therefore, the probability that the car will idle roughly after 5,000 miles is $0.3439$

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