# Chapter 12 - Data Analysis and Probability - Chapter Test - Page 779: 19

Yes

#### Work Step by Step

Let A and B be mutually exclusive events (given). When we add the probability of event A to the probability of event B, we will have overlap (there will be at least one instance of both events happening). Thus, when we subtract the probability of events A and B from the sum we have (P(A) + P(B)), we remove half of the duplicated part of the overlap from the two events. Example: We flip a coin and roll a number cube. We want a heads on the coin and the number 3 to be rolled. P(heads on coin) = 1/2 P(3 on number cube) = 1/6 The 12 possible outcomes of the two events are as follows (where H is heads, T is tails, and the number is the number rolled): 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, and 6T. (There is one result that has both heads and the number 3--3H.) P(heads or 3) = P(heads) + P(3) - P(heads and 3) $7/12 = 6/12 + 2/12 - 1/12$ $7/12 = 8/12 - 1/12$ $7/12 = 7/12$

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