Need help solving

Question

The 3 set Venn diagram here shows the number of people in each set. Use this to find the probability of observing the given set.

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Answer 1

Hi Lakotah,

First, add the total of all units in the Venn Diagram:

(8+7+1+6+4+14+10+6)= 56

Now, the question asked for A intersection (B U C)--sorry, no intersection key here. Now, (B U C)--read as "B union C"--includes everything except the number A only and the number outside the set altogether, BUT we want the intersection A intersection (B U C). That includes only the sections in the center of the diagram., the members of both A and (B U C). This is:

n(A intersection (B U C) = 7 + 1 + 6 = 14

Now, we're not done yet, because the question asked for the probability. To compute this, take:

n(A intersection (B U C)/Total

P(A intersection (B U C)) = 14/56 = 1/4

I hope this helps.