Collapsing Probabilities: Part Deux — for Part Un, Click Here
This one I’m only doing with the “Collapsing Probabilities” technique. You’re welcome to do it by making your choice first, then multiplying by the number of potential choices. It’s just that I won’t. You can e-mail me if you need your hand held.
Here’s the question:
Company X employs 400 people and Company Y employs 300 people. Twenty-five people in Company X have spouses who are employed by Company Y. What is the Probability that, if we select a person from Company X and a person from Company Y, we will select a couple who are married to each other?
This doesn’t look too bad. If we’re limiting our group to the people from Company X who have spouses within Company Y, we find our Probability for the first selection to be:
Working from this standpoint, let’s imagine that Jane works for Company X and her spouse, Lydia, works for Company Y. What’s the appropriate question to ask here?
Let’s step back for a moment. This isn’t some key party taking place in a conversation pit in 1970s suburbia. If we select a married person from Company X, it stands to reason we’re selecting the spouse from Company Y. Like one single person Y corresponding to one single person X, yes?
That’s the practical meaning of “collapsing Probability.”
In essence, that makes the question clearer: What is the Probability that we select Lydia from Company Y? That presents…
Given this, we can see that our ultimate Probability is:
(25/400)*(1/300) = (1/16)*(1/300) = 1/4800
Got it? Good.
Luckily, this is the last major technique we’ll see in our discussion of GMAT Probability. What next? Why example problems, of course.
It’s always important to look at specific example problems to see how to tackle more complex ideas in a live setting. That’s what the focus of the next few blog posts will be…
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