Question

Belle is a ranger at Roaring Rivers State Park. In surveying the hiking trails for a park brochure, she found that 48% of the trails are rated as easy and 63% of the trails are rated as easy or have a scenic overlook. If 11% of the trails are rated as easy and have a scenic overlook, what is the probability that a randomly selected trail has a scenic overlook?

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Answer 1

We are given the following information:
P(E) = 0.48 (48% of trails are rated as easy)
P(E ∪ O) = 0.63 (63% of trails are either easy or have a scenic overlook)
P(E ∩ O) = 0.11 (11% of trails are both easy and have a scenic overlook)

We can use these probabilities to calculate P(O), the probability of a trail having a scenic overlook, as follows:

P(E ∪ O) = P(E) + P(O) - P(E ∩ O)

Substituting the given values:

0.63 = 0.48 + P(O) - 0.11

Now, let's solve for P(O):

0.63 - 0.48 + 0.11 = P(O)
0.26 = P(O)

Therefore, the probability that a randomly selected trail has a scenic overlook is 0.26 or 26%.