Final answer:
The correct probability expression for a person who does yoga type A or B but not C is P(A ∪ B) - P((A ∪ B) ∩ C). It involves adding the probabilities of A and B, then subtracting the intersection with C.
Step-by-step explanation:
The question asks for the probability that a randomly selected person does yoga of type A or B but not C. The correct expression to find this probability is P(A ∪ B) - P((A ∪ B) ∩ C). This expression adds the probabilities of A and B and subtracts the probability of both A or B and C occurring, effectively removing those who do yoga type C from the count.
To calculate it based on the given information, follow these steps:
- Find the probability of doing yoga type A or B, which is P(A ∪ B).
- Find the probability of doing both yoga type A or B and C, which is P((A ∪ B) ∩ C).
- Subtract the second probability from the first to exclude those who do type C: P(A ∪ B) - P((A ∪ B) ∩ C).
None of the given options a) P(A∪B∩C), b) P(A∩B∪C), c) P(A∩B∪C), d) P(A∪B∩C) correctly represent the needed probability. They are all different combinations that don't fit the question's criteria.