Çözüldü Probability of Mutually Inclusive Events - Complementary Events

A solved example From the University of South Carolina

The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35%. Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work. Calculate the probability that a visit to a PCP’s office results in both lab work and referral to a specialist.
A) 0.05
B) 0.12
C) 0.18
D) 0.25
E) 0.35

Let R = referral to a specialist and L = lab work. Then;
P[R ∩ L] = P[R] + P[L] - P[R ∪ L] = P[R] + P[L] - 1 + P[ (R ∪ L)^c ]
P[R ∩ L] = P[R] + P[L] - 1 + P[ R^c ∩ L^c ]
P[R ∩ L] = 0.3 + 0.4 - 1 + 0.35 = 0.05.

https://people.stat.sc.edu/Tebbs/stat512/ExamP_sample_questions.pdf (Page 2, Question 2)
Solutions: https://people.stat.sc.edu/Tebbs/stat512/ExamP_solutions.pdf (Page 2, with some changes)