The probability of visiting the zoo is 0.80. The probability of visiting the caverns is 0.55. The probability of visiting both is 0.42. What is the probability of the visiting the zoo or the caverns?
To find the probability of visiting the zoo or the caverns, we can use the formula:
P(Zoo or Caverns) = P(Zoo) + P(Caverns) - P(Zoo and Caverns)
P(Zoo or Caverns) = 0.80 + 0.55 - 0.42
P(Zoo or Caverns) = 1.33 - 0.42
P(Zoo or Caverns) = 0.91
Therefore, the probability of visiting the zoo or the caverns is 0.91.
To find the probability of visiting the zoo or the caverns, we need to use the principle of addition, which states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.
Let's denote the probability of visiting the zoo as P(Z) = 0.80, and the probability of visiting the caverns as P(C) = 0.55. The probability of visiting both the zoo and the caverns is P(Z ∩ C) = 0.42.
Now, we can use the principle of addition to find the probability of visiting the zoo or the caverns:
P(Z U C) = P(Z) + P(C) - P(Z ∩ C)
Substituting the given values, we have:
P(Z U C) = 0.80 + 0.55 - 0.42
Calculating this expression:
P(Z U C) = 0.95
Therefore, the probability of visiting the zoo or the caverns is 0.95, or 95%.
To find the probability of visiting either the zoo or the caverns, we can use the formula for the probability of the union of two events.
P(Zoo or Caverns) = P(Zoo) + P(Caverns) - P(Zoo and Caverns)
Given:
P(Zoo) = 0.80
P(Caverns) = 0.55
P(Zoo and Caverns) = 0.42
Substituting the values into the formula:
P(Zoo or Caverns) = 0.80 + 0.55 - 0.42
P(Zoo or Caverns) = 0.93
Therefore, the probability of visiting either the zoo or the caverns is 0.93.