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In nine independent trials, what is the probability that

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In nine independent trials, what is the probability that

by BTGmoderatorLU » Wed Apr 24, 2019 3:16 pm

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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.

The OA is D
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Apr 24, 2019 11:01 pm

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BTGmoderatorLU wrote:Source: Magoosh

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.

The OA is D
Instead of calculating the probability that Outcome A happens at least once, it's better we calculate the probability that Outcome A does not happen even once; once we get this value, we would deduct it from 1 and get the answer.

Probability that Outcome A happens at least once = 1 - Probability that Outcome A does not happen even once in 9 trials

Let's take each statement one by one.

1) The probability that Outcome A does not happen even once in any of the nine trials is 0.026.

=> Probability that Outcome A happens at least once = 1 - Probability that Outcome A does not happen even once in 9 trials = 1 - 0.026 = A unique value. Sufficient.

2) The probability of Outcome A resulting in a single trial is 1/3.

Probability that Outcome A does not happen in a single trial = 1 - 1/3 = 2/3

Probability that Outcome A does not happen even once in 9 trials = (2/3)^9

Probability that Outcome A happens at least once = 1 - (2/3)^9 = A unique value. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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by deloitte247 » Sat Apr 27, 2019 12:28 pm

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Probability of favorable outcome + probability of unfavorable outcome = 1
Probability of favorable outcome = 1 - probability of favorable outcome
Probability that outcome A happens at least once = 1 - probability that outcome A never happens

Statement 1
The probability that outcome A doesn't even happen even once in any of the nine trials is 0.026
Probability that outcome A happens at least once = 1 - 0.026 = 0.974

Statement 1 is SUFFICIENT.

Statement 2
The probability of outcome A resulting in a single trial is 1/3
The probability that the outcome doesn't happen in a single trial.
$$\frac{1}{1}-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}$$

Probability that the outcome A happens in all the 9 trials
$$\left(\frac{2}{3}\right)^9=\frac{2^9}{3^9}=\frac{512}{19683}=0.026$$

Probability that outcome A happens at least once = 1- 0.026 = 0.974

Statement 2 is also SUFFICIENT.
Both statement alone are SUFFICIENT.

$$answer\ is\ Option\ D$$
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