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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]  25 Feb 2017, 09:28
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Question Stats:

86% (00:27) correct 13% (00:22) wrong based on 15 sessions

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]  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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Joined: 18 Apr 2015
Posts: 5845
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Kudos [?]: 1144 [0], given: 5448

Re: A certain experiment has three possible outcomes. The outco [#permalink]  26 Nov 2017, 06:54
Expert's post
Explanation

$$P + \frac{P}{2} + \frac{P}{4} = 1$$

$$4P + 2P + P = 4$$

$$P = \frac{4}{7}$$

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Re: A certain experiment has three possible outcomes. The outco   [#permalink] 26 Nov 2017, 06:54
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