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A certain experiment has three possible outcomes. The outcomes are mut

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A certain experiment has three possible outcomes. The outcomes are mut  [#permalink]

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New post 26 Jun 2018, 21:09
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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) \(\frac{5}{7}\)

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Re: A certain experiment has three possible outcomes. The outcomes are mut  [#permalink]

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New post 26 Jun 2018, 22:06
Bunuel 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) \(\frac{5}{7}\)



Mutually exclusive - In probability , two mutually exclusive or disjoint events MEANS both cannot occur together. example : a single coin toss, which can result in either heads or tails, but not both.

So this means there is no interaction of the 3 events and also there are only these three outcomes possible..
So addition of their probabilities should equal 1..
So \(P+\frac{P}{2}+\frac{P}{4}=1.......\frac{7P}{4}=1.........P=\frac{4}{7}\)

D
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Re: A certain experiment has three possible outcomes. The outcomes are mut  [#permalink]

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New post 26 Jun 2018, 22:28

Solution



Given:
    • A certain experiment has three possible outcomes
    • The outcomes are mutually exclusive and have probabilities \(p\), \(\frac{p}{2}\), and \(\frac{p}{4}\), respectively

To find:
    • The value of p

Approach and Working:
As the outcomes are mutually exclusive, any two or all 3 of them cannot occur at the same time

Also, as there are only 3 outcomes, the sum of their probabilities should be equal to 1
    • Therefore, we can write, \(p + \frac{p}{2} + \frac{p}{4} = 1\)
    Or, \(\frac{7p}{4} = 1\)
    Or, \(p = \frac{4}{7}\)

Hence, the correct answer is option D.

Answer: D
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Re: A certain experiment has three possible outcomes. The outcomes are mut  [#permalink]

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New post 11 Jul 2018, 09:18
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Another way is to think of ratios. We need a ratio of 4:2:1 for the outcomes to respectively have probabilities p, p/2 and p/4. So the probability p of having the first outcome is 4/(4+2+1) = 4/7.
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Re: A certain experiment has three possible outcomes. The outcomes are mut &nbs [#permalink] 11 Jul 2018, 09:18
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