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A certain experiment has three possible outcomes. The outcom

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A certain experiment has three possible outcomes. The outcom [#permalink] New post 25 Feb 2017, 09:28
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A certain experiment has three possible outcomes. The outcomes are mutually exclusive and have probabilities \(p\), \(\frac{p}{2}\), and \(\frac{p}{4}\), respectively. What is the value of \(p\)?



A) \(\frac{1}{7}\)

B) \(\frac{2}{7}\)

C) \(\frac{3}{7}\)

D) \(\frac{4}{7}\)

E) \(\frac{5}{7}\)
[Reveal] Spoiler: OA

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Re: A certain experiment has three possible outcomes. The outcom [#permalink] New post 04 Mar 2017, 17:51
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Explanation

The outcomes are mutually exclusive, meaning that they cannot happen at the same time. So the three outcomes are separate.

Because there are only three outcomes, we know that one of these outcomes will definitely happen. Thus, the probability of the three outcomes must add up to 1 (representing 100% certainty):

\(p + \frac{p}{2} +\frac{p}{4}=1\).

We solve for p and find \(p = \frac{4}{7}\).

Hence option D is correct.
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Re: A certain experiment has three possible outcomes. The outco [#permalink] New post 26 Nov 2017, 06:54
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Explanation

\(P + \frac{P}{2} + \frac{P}{4} = 1\)

\(4P + 2P + P = 4\)

\(P = \frac{4}{7}\)

D is the answer
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Re: A certain experiment has three possible outcomes. The outcom [#permalink] New post 15 Jun 2019, 06:37
Just because the outcomes are mutually exclusive, they should happen one after the other.
But all the outcomes would have to add up to 100% probability. 100% means a probability of 1.
P+P/2+P/4=1
4P+2P+P=4
7P=4
P=4/7
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Re: A certain experiment has three possible outcomes. The outcom [#permalink] New post 15 Jun 2019, 08:06
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Carcass wrote:


A certain experiment has three possible outcomes. The outcomes are mutually exclusive and have probabilities \(p\), \(\frac{p}{2}\), and \(\frac{p}{4}\), respectively. What is the value of \(p\)?



A) \(\frac{1}{7}\)

B) \(\frac{2}{7}\)

C) \(\frac{3}{7}\)

D) \(\frac{4}{7}\)

E) \(\frac{5}{7}\)


In case anyone is wondering why we need the condition that the outcomes are mutually exclusive, here's why:

If the outcomes were NOT mutually exclusive, then that would means that some outcomes could occur at the same time, and this would mean that the 3 probabilities need not add to 1.

Here's an example:
Let's say we're rolling 1 standard die (with integers 1 to 6), and we want to examine 3 probabilities:
P(the number is less than 7)
P(the number is less than 8)
P(the number is even)

Notice that ALL 3 of these outcomes can occur at the same time.
The individual probabilities are:

P(the number is less than 7) = 1
P(the number is less than 8) = 1
P(the number is even) = 0.5

As you can see, since the outcomes are NOT mutually exclusive, we can't conclude that the sum of the three probabilities = 1

Cheers,
Brent
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Re: A certain experiment has three possible outcomes. The outcom   [#permalink] 15 Jun 2019, 08:06
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