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Statistical probability, help!

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by ellexay » Sat Feb 07, 2009 12:42 pm
Patrons at a certain restaurant can select two of three appetizers--fruit, soup, and salad--along with two of three vegetables--carrots, squash, and peas. What is the statistical probability that any patron will select fruit, salad, squash, and peas?

Official answer: 1/9
My answer: 1/2

The correct answer is B. In each set are three distinct member pairs. Thus the probability of selecting any pair is one in three, or img/img178.png. Accordingly, the probability of selecting fruit and salad from the appetizer menu along with squash and peas from the vegetable menu is img/img179.png.



I got 1/2 from: (3C2)(3C2) all divided by (3^2 + 3^2), to account for the number of possible outcomes.

Please tell me why my answer/approach is wrong! Thank you. =)
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by sureshbala » Sat Feb 07, 2009 12:48 pm
Definitely the total number of favorable cases here is 1 since we have to select a fruit, salad, squash, and peas.

Coming to the total number of chances it is nothing but 3C2 x 3C2 = 9.

So the probability is 1/9.
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by lunarpower » Sun Feb 08, 2009 11:13 am
you can also solve this problem by reframing "select two of three options" as "select the one option that you DON'T want".

this reframing makes this problem a lot easier:
* total possibilities: you DON'T want ONE of the 3 appetizers, and you DON'T want ONE of the 3 vegetables. therefore, there are 3 x 3 = 9 ways to choose what you DON'T want.
* there is only 1 "success", which is NOT getting soup and NOT getting carrots.

therefore, probability = 1/9.

--

in your approach, (3c2)^2 should be the denominator, as that's the total number of ways in which to choose two appetizers and two vegetables.

i'm not sure where you got 3^2 + 3^2, or what it's supposed to represent, but there are at least two things wrong with it: (a) 3^2 only makes sense if you're allowed to repeat your choice (i.e., "salad and salad"), and (b) adding doesn't make sense, either, because you aren't choosing between alternatives ("OR"). remember, AND goes with multiplication, and OR goes with addition.
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by Alara533 » Sun Feb 08, 2009 12:29 pm
Probability of selecting fruit and salad from - fruit, soup, and salad is 1/3.
Probability of selecting Squash and Peas from - carrots, squash, and peas is 1/3.

P (A and B) = P(A) * P(B) = 1/3 * 1/3 = 1/9.
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