# At the Stop 'n Go tune-up and brake

At the Stop 'n Go tune-up and brake shop, the manager has found that an SUV will require a tune-up with a probability of 0.6, a brake job with a probability of 0.1 and
both with a probability of 0.02. What is the probability that an SUV requires neither type of repair?

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user_27qwe

Two events are mutually exclusive when both events cannot happen at the same time.

Thus, the probability of either event happening is

Two events are said to the mutually inclusive when both the events can happen simultaneously at the same time.

The probability of either event happening is

Let x be the event that SUV requires a tune-up

$P\left(x\right)=0.6$

Let y be the event that SUV requires a brake job

$P\left(y\right)=0.1$

SUV requires a tune-up and a brake job

$P\left(x\cap y\right)=0.02$

As both events are mutually inclusive, that is, both events can happen at the same time.

The probability that SUV requires either tune-up or bore job is

$P\left(x\cup y\right)=P\left(x\right)+P\left(y\right)-P\left(x\cap y\right)$

$=0.6+0.1-0.02$

$P\left(x\cup y\right)=0.68$

In mutually inclusive events to find the probability of either event happening, you can add the probability of the individual events and subtract the probability of both events at the same time.