Carcass wrote:
If the probability that Mike will miss at least one of the ten jobs assigned to him is 0.55, then what is the probability that he will do all ten jobs?
(A) 0.1
(B) 0.45
(C) 0.55
(D) 0.85
(E) 1
When it comes to probability questions involving
at least, it's best to consider using the
complement.
That is,
P(Event A happening) = 1 - P(Event A not happening)So, here we get: P(missing AT LEAST one job) = 1 -
P(not missing AT LEAST one job)What does it mean to
not miss at least one job?
It means missing ZERO jobs.
Or we can say that it means doing ALL 10 jobs.
So, we can write: P(missing AT LEAST one job) = 1 -
P(doing all 10 jobs )Substitute to get: 0.55 = 1 -
P(doing all 10 jobs )Solve to get:
P(doing all 10 jobs ) = 0.45Answer: B
Cheers,
Brent