If the probability that Mike will miss at least one of the ten jobs as

Question

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

BrentGMATPrepNow · Accepted Answer

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 ) = 0.45

Answer: B

Cheers,
Brent

Archit3110 · Answer

P of missing = 0.55
doing job = 1-0.55
IMO B
0.45

CrackverbalGMAT · Answer

This problem can be solved very easily if you apply the principle of Probability(At least one).
 Probability (At least one) = 1 – Probability (None).

Therefore, Probability (Mike will miss at least one job) = 1 – Probability (Mike misses none of them).

Re-organising the equation, we have,
Probability (Mike does all ten jobs) = 1 – Probability (Mike will miss at least one job) {note that missing none of them is equivalent to doing all the ten jobs}

Substituting the value of the probability given in the question, we have,
Probability (Mike does all ten jobs) = 1 – 0.55 = 0.45.

The correct answer option is B .

Hope that helps!

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