Question

In: Statistics and Probability

There are 3 car mechanics. They all fix a number of cars each year. Each mechanic...

There are 3 car mechanics. They all fix a number of cars each year. Each mechanic (Mike, John, and Nick) have an rate for failing car parts. Find the probability that a car part fails. Hint. rate # of failed cars/ car work per person i.e. 2/40 for Mike.

Mechanic	Portion of Car Work	# of failed cars
Mike	40	2
John	10	3
Nick	50	4

Also, if the car part fails, find the probability that the car was produced by

A. Mike

B. John

C. Nick

Expert Solution

a)

P(car part fails) = P(part fails|it is fixed by mike) +P(part fails|it is fixed by john) + P(part fails|it is fixed by nick)

= 2/40 + 3/10 + 4/50

= 43/100

= 0.43

b)

i)

P(it is fixed by mike | car part fails) = (2/40)/0.43

= 5/43

ii)

P(it is fixed by john | car part fails) = (3/10)/0.43

= 30/43

iii)

P(it is fixed by nick | car part fails) = (4/50)/0.43

= 8/43

orchestra answered 2 years ago

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