A study by the National Park Service revealed that 50% of the vacationers going to the Rocky Mountain region visit Yellowstone Park, 40% visit the Tetons and
35% visit both. What is the probability that a vacationer will visit at least one of these magnificent attractions?
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A. B. C. D. E.B
0.5 + 0.4 - 0.35 = 0.55
To solve this problem, we can use the principle of inclusion-exclusion. Let's break down the given information:
Now, let's calculate the probability that a vacationer will visit at least one of these attractions.
To find this probability, we need to add the individual probabilities of visiting Yellowstone Park and the Tetons and then subtract the probability of visiting both, as we counted it twice when adding the individual probabilities. The formula for inclusion-exclusion is:
P(A or B) = P(A) + P(B) - P(A and B)
Let's calculate it step by step:
P(Yellowstone Park) = 50% = 0.50 P(Tetons) = 40% = 0.40 P(Yellowstone Park and Tetons) = 35% = 0.35
Now, let's substitute these values into the formula:
P(Visit at least one attraction) = P(Yellowstone Park) + P(Tetons) - P(Yellowstone Park and Tetons) P(Visit at least one attraction) = 0.50 + 0.40 - 0.35 P(Visit at least one attraction) = 0.90 - 0.35 P(Visit at least one attraction) = 0.55
Therefore, the probability that a vacationer will visit at least one of these magnificent attractions is 0.55.
The correct answer is B. 0.55.