Considering the definition of probability, the probability that the family visits the museum or rides the ferry is 81%.
Definition of Probabitity
Probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
Union of events
The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.
Events and probability in this case
Let A be the event that a family visits the City Museum, and B be the event that a family rides the Three Rivers Ferry. The given probabilities are:
P(A)= 0.46
P(B)= 0.47
P(A and B)= P(A∩B)= 0.12
In this case, considering the definition of union of eventes, the probability that a course has a final exam or a research project is calculated as:
P(A∪B)= P(A) + P(B) -P(A∩B)
P(A∪B)= 0.46 + 0.47 -0.32
P(F∪R)= 0.81= 81%
Finally, the probability that the family visits the museum or rides the ferry is 81%.