Question: A basic question about probability. Details below.

The probability of event E happening is 0.3. The probability of event F happening is 0.5. The probability of both E and F happening is 0.1. What is the probability that *either* E or F (or both) happens?
Answer 1/2
Think of E and F as circles within a rectangle of area 1.

Since Pr(E) = 0.3, the circle E will have area 0.3. Similarly, circle F will have area 0.5.

Pr(E intersect F) is the area within both circles E and F simultaneously. In other words, it's the overlap. We are told Pr(E intersect F) = 0.1.

Our goal is to find Pr(E U F), which is the total area that's in at least one of the circles (the union of the two areas).

(area covered by circle E) = 0.3
(area covered by both circles E and F) = 0.1

Therefore:

(area covered by circle F but NOT by circle E) = (area of circle F) - (area of circle F that is also in circle E) = 0.5 - 0.1 = 0.4

Total area covered by the two circles:

(area covered by circle E) + (area covered by circle F but NOT by circle E) = 0.3 + 0.4 = 0.7

This is the desired answer; Pr(E U F) = 0.7.
by fantom
Answer 2/2
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