Problem related to Mutually Exclusive Events

Screen Link:
https://app.dataquest.io/m/1015/probability-rules-practice-problems/3/mutually-exclusive-events

I was working on the 3rd question in this screen and I’m confused by the hint provided, specifically the second point:
image

The way I see the problem is, 132 customers were given travel forms respectively to fill, with two options:

  • summer vacation
  • winter vacation

Of those 132, 64 selected the first option, 21 selected the second option and 15 selected both options. The remaining selected neither . So it seems straightforward that the number of people who didn’t buy a vacation at all must be 132-64-21-15.

What is the hint trying to get to?

Cheers

For a simple example, out of 15 people -

selection
S
W
S
W
W
S, W

So, what you are assuming is that there are 3 distinct categories here -

  • 2 people bought a summer vacation
  • 3 people bought a winter vacation
  • 1 person bought both

The above is correct if the events are mutually exclusive.

In the content they specify that the events are mutually non-exclusive they are calculating it as -

  • 3 people in total bought a summer vacation (2 individual S, and 1 from S, W)
  • 4 people in total bought a summer vacation (3 individual W, and 1 from S, W)
  • 1 person bought both

In your case, when you try to calculate who didn’t buy a vacation it would be 15 - 2 - 3 - 1.

In their case, it would be 15 - (3 + 4 - 1). We subtract 1 because we already included that person for both of the individual categories (so twice).

But the content makes the distinction by stating that the events are mutually non-exclusive. It can be a bit confusing because the experiment design and the results (survey) make it seem that 3 categories are being tracked separately and values are being accumulated exclusively for each category. And, as per me, how the data was collected/tracked/stored could be better clarified to help beginners better understand the topic.

Since it’s specified they are mutually non-exclusive, then that’s what you should work with. If it’s not specified, then that’s when other things should be taken into account instead of making assumptions.

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@the_doctor thank you very much! :smiley:

It can be a bit confusing because the experiment design and the results (survey) make it seem that 3 categories are being tracked separately and values are being accumulated exclusively for each category.

As you mentioned, the problem is with the way the question is framed. I saw it as three mutually exclusive categories. I did not connect it with the topic at hand.

Your explanation is perfect and makes sense.

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