There are two species of plants that live along the ridge line of Old Rag, which is a mountain here in Virginia. The probability of observing the first species is 0.61, while the probability of observing the second species is 0.08. The probability of observing them growing together (i. e. right next to one another) is 0.28. When you go for a hike along this ridge line, what is the probability of observing one species or the other but not both together

Question

Mathematics

Jaden Brady

20 July, 22:25

There are two species of plants that live along the ridge line of Old Rag, which is a mountain here in Virginia. The probability of observing the first species is 0.61, while the probability of observing the second species is 0.08. The probability of observing them growing together (i. e. right next to one another) is 0.28. When you go for a hike along this ridge line, what is the probability of observing one species or the other but not both together

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Charlee Sparks · Answer 1

0.13

Step-by-step explanation:

First let's find the probability of finding the first species or the second species:

P (A or B) = P (A) + P (B) - P (A and B)

P (A or B) = 0.61 + 0.08 - 0.28

P (A or B) = 0.41

Then, to find the probability of finding one or another but not both, we just need the symmetric difference of the events, that is: P (A or B) - P (A and B):

P (A or B) - P (A and B) = 0.41 - 0.28 = 0.13