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 $0.3439$