Chapter 10 Counting Methods and Probability - 10.4 Find Probabilities of Disjoint and Overlapping Events - 10.4 Exercises - Skill Practice - Page 711: 40

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We can see that there are 8 dots in A, 7 dots in B, 3 dots in A and B, and 12 dots in A or B. Thus we have $P(A)=8\\P(B)=7\\P(A ∩ B)=3\\P(A \cup B)=12$ Obtain: $P(A)+P(B)=P(A ∩ B)+P(A \cup B)\\8+7=12+3\\15=15$ Since $15=15$ is true, $P(A) = P(B)= P(A or B)= P(A and B)$