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probabilities of independent events

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probabilities of independent events

by charlieh65 » Wed Jan 07, 2015 6:13 pm
This may be a stupid question, but I'm driving myself crazy trying to figure out what I'm doing wrong so hopefully you can help!

Alison has a 1/4 probability of going to college. Brandon has a 1/2 probability of going to college. Charlie has a 1/4 probability of going to college. What is the probability that Alison, Brandon, or Charlie will go to college?


I keep thinking back to..."AND means MULTIPLY, OR means ADD." But of course there isn't a 100% chance that one of them is going to college. help!
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by [email protected] » Wed Jan 07, 2015 6:19 pm
Hi charlieh65,

When it comes to probability questions, you can either calculate what you WANT to have happen OR you can calculate what you DON'T WANT to have happen, then subtract this result from the number 1.

Here, the question is worded in such as way to as make me think that its "intent" is to ask for the probability that AT LEAST ONE of the three goes to college. The wording is a big vague though - it's intent might be to ask for the probability that JUST ONE of the three goes to college.

Assuming that it's asking for AT LEAST ONE, it's easiest to calculate the probability that NONE of them will go to college, then subtract that result from 1.

(Not Alison)(Not Brandon)(Not Charlie) = (3/4)(1/2)(3/4) = 9/32

So the probability is 9/32 that NONE of them will go to college. This means that.....

1 - 9/32 = 23/32 is the probability that AT LEAST ONE will go to college.

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Last edited by [email protected] on Thu Jan 08, 2015 11:15 am, edited 1 time in total.
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by MartyMurray » Wed Jan 07, 2015 7:14 pm
charlieh65 wrote:This may be a stupid question, but I'm driving myself crazy trying to figure out what I'm doing wrong so hopefully you can help!

Alison has a 1/4 probability of going to college. Brandon has a 1/2 probability of going to college. Charlie has a 1/4 probability of going to college. What is the probability that Alison, Brandon, or Charlie will go to college?


I keep thinking back to..."AND means MULTIPLY, OR means ADD." But of course there isn't a 100% chance that one of them is going to college. help!
Just so you have it clear, or means add when the probabilities we are talking about are parts of a set of related mutually exclusive events. For instance, if the question asked "What is the probability of Alison going to college or not going to college?" then you could add the two probabilities and get 100%. The two events are mutually exclusive parts of the set of Alison's possible college decisions.

If you were drawing a card from a deck and wanted to know the chance of getting the king of spades or the jack of spades, you could add the two, 1/52 + 1/52, and get 2/52, which makes sense when you think about it. Each probability is an element of the set of probabilities of mutually exclusive results of drawing one card from the deck. All the probabilities in that set add up to 100 percent. If within that set there are multiple events considered favorable, you can just add their probabilities to determine the probability of a favorable event occurring.

On the other hand, if you were asking "In drawing one card from each of two decks what is the chance of getting at least one of the following, the jack of spades from the first deck or the king of spades from the other?" you can't just add their probabilities. The two events are not mutually exclusive elements in the same set of probabilities.
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by [email protected] » Thu Jan 08, 2015 11:21 am
Hi Charlieh65,

I mentioned the "2nd way" of interpreting what the question was asking for - the probability that JUST one gets into college. Here's how THAT calculation would look:

It's worth noting that for JUST ONE to get in....the other two CANNOT get in, so we have to factor that into the calculations:

1) Allison gets in, the others don't =
(Allison in)(Not Brandon)(Not Charlie) =
(1/4)(1/2)(3/4) = 3/32

2) Brandon gets in, the others don't =
(Not Allison)(Brandon in)(Not Charlie) =
(3/4)(1/2)(3/4) = 9/32

3) Charlie gets in, the others don't =
(Not Allison)(Not Brandon)(Charlie in) =
(3/4)(1/2)(1/4) = 3/32

Here, we have 3 different outcomes that fit what we "WANT", so the overall probability is...

3/32 + 9/32 + 3/32 = 15/32 that JUST ONE of the three will get into college.

GMAT assassins aren't born, they're made,
Rich
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