Question

Fill in the blanks in the following table: P(A) P(B) P(A ∩ B) P(A ∪ B) (i) 1/3 1/5 1/15 ....... (ii) 0.35 ...... 0.25 0.6 (iii) 0.5 0.35 ....... 0.7 Select the correct answer from above options

Answer 1

(i) By definition of P (A or B) under axiomatic approach we know that: P (A ∪ B) = P (A) + P (B) – P (A ∩ B) By using data from table, we get: ∴ P (A ∪ B) = 1/3 + 1/5 – 1/15 = 8/15 – 1/15 = 7/15 (ii) By definition of P (A or B) under axiomatic approach we know that: P (A ∪ B) = P (A) + P (B) – P (A ∩ B) P (B) = P (A ∪ B) + P (A ∩ B) – P (A) By using data from table, we get: ∴ P (B) = 0.6 + 0.25 – 0.35 = 0.5 (iii) By definition of P (A or B) under axiomatic approach we know that: P (A ∪ B) = P (A) + P (B) – P (A ∩ B) P (A ∩ B) = P (B) + P (A) – P (A ∪ B) By using data from table, we get: ∴ P (A ∩ B) = 0.5 + 0.35 – 0.7 = 0.15 Hence the table is: