Question

Please help!!

What is the probability that either event will occur?
8
A
3
B
10
12
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.

Answer 1

P(A or B) = 0.64

Explanation:

You want the probability that A or B will occur, given the occurrence counts shown in the Venn diagram.

A or B

The formula shown in the diagram shows you how to compute the probability. It can be simpler than that.

The number of counts in the circles A or B is ...

8 + 3 + 10 = 21.

The total number of counts in the diagram is ...

21 +12 = 33

Then ...

P(A or B) = (counts of A or B)/(total counts) = 21/33 = 7/11 = 0.6363...

Rounded to hundredths, the probability is ...

P(A or B) = 0.64

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Additional comment

If you use the formula, it tells you ...

P(A or B) = 11/33 +13/33 -3/33 = 21/33 ≈ 0.64

Note that we have added 3/33 to the sum twice and subtracted it once. The computation shown above eliminates the extra addition and subtraction.

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