A = Event that it rains on Thursday
B = Event that it rains on Friday
C = Event that it rains on Saturday
Here, P(A) = 0.8, P(B) = 0.7 and P(C) = 0.6 are given.
A, B and C are independent events.
∴ P(A ∩B) = P(A) ∙ P(B) = 0.8 × 0.7 = 0.56
P(A ∩ C) = P(A) ∙ P(C) = 0.8 × 0.6 = 0.48
P(B ∩ C) = P(B) ∙ P(C) = 0.7 × 0.6 = 0.42
P(A ∩ B ∩ C) = P(A) ∙ P(B) ∙ P(C)
= 0.8 × 0.7 × 0.6 = 0.336
Now, A ∪ B ∪ C = Event that it rains on at least one of the three days in the next week
According to the law of addition of probability,
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(A ∩ C) –
P(B ∩ C) + P(A ∩ B ∩ C)
= 0.8 + 0.7 + 0.6 – 0.56 – 0.48 – 0.42 + 0.336
= 0.976