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In nine independent trials, what is the probability that Outcome A happens at least once?

(1) The probability that Outcome A does not happen even once in any of the nine trials is 0.026 (2) the probability of Outcome A resulting in a single trial is 1/3.

In nine independent trials, what is the probability that Outcome A [#permalink]

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18 Feb 2015, 07:27

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Probability (Outcome A happens at least once)+probability(Outcome A does not happen even once)=1. Statement 1= Sufficient. statement 2= We know probability of A=1/3, p(A')=2/3 with these we can find out all the cases when A occurs at least once.sufficient.

In nine independent trials, what is the probability that Outcome A happens at least once?

(1) The probability that Outcome A does not happen even once in any of the nine trials is 0.026 (2) the probability of Outcome A resulting in a single trial is 1/3.

Kudos for a correct solution.

Probability of Favorable Outcome + Probability of Unfavorable Outcome = 1

i.e. Probability of Favorable Outcome = 1 - Probability of Unfavorable Outcome

i.e. probability that Outcome A happens at least once = 1 - Probability that Outcome A never happens

Statement 1: P (A never happens) = 0.026 i.e. P (A happens atleast once) = 1- 0.026 = 0.974 SUFFICIENT

Statement 2: probability of Outcome A resulting in a single trial is 1/3 i.e. probability of Outcome A Not happen in a single trial is 1-(1/3) = 2/3 i.e. Outcome A never happens in all 9 trials = (2/3)^9 = 0.026 i.e. P (A happens atleast once) = 1- 0.026 = 0.974 SUFFICIENT

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Re: In nine independent trials, what is the probability that Outcome A [#permalink]

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18 Feb 2015, 08:43

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Here we go:

St1: The probability that Outcome A does not happen even once in any of the nine trials is 0.026

We have been asked the probability that Outcome A happens at least once.

This can be calculate ---> (1 - 0.026)

Hence St1 is sufficient

St2 : the probability of Outcome A resulting in a single trial is 1/3. We can also calculate the probability of Outcome A not resulting in a single trial : (1 - 1/3) = 2/3

So we can find easily calculate the probability that Outcome A happens at least once by using above information.

In nine independent trials, what is the probability that Outcome A happens at least once?

(1) The probability that Outcome A does not happen even once in any of the nine trials is 0.026 (2) the probability of Outcome A resulting in a single trial is 1/3.

We know there are nine trials. To figure out the probability that Outcome A happens at least once, we would need a way to figure out the probability of A, P(A).

Statement #1: this statement gives us the complement. The complement of (Outcome A happens at least once) is (Outcome A does not happen at all). Complementary probabilities have a sum of 1 — P(not K) = 1 – P(K). Therefore, using the complement rule, we could figure out that P(A happens at least once) = 1 – P(A doesn’t happen at all) = 1 – 0.026 = 0.974 This information allows us to answer the prompt question. This statement, alone and by itself, is sufficient.

Statement #2: this statement gives us P(A), which would allow us to calculate the probability that A happens at least once in nine trials. This statement, alone and by itself, is sufficient.

Re: In nine independent trials, what is the probability that Outcome A [#permalink]

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24 Feb 2015, 09:02

Ans Is D coz of the following Statement 1 is sufficient as this is giving us the case of when an event is not happening ...question asked is when the event happens atleast once i.e 1-(when the event does not happens). Statement 2 is sufficient cause as we know the probability of event happening so we can find when atleast once.

Re: In nine independent trials, what is the probability that Outcome A [#permalink]

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30 Sep 2017, 11:21

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