Question

The probability that a new railway bridge will get an award for its design is 0.48, the probability that it will get an award for the efficient use of materials is 0.36, and that it will get both awards is 0.2. What is the probability, that 

(i) it will get atleast one of the two awards

(ii) it will get only one of the awards

Answer 1

Given P(A) = 0.48, P(B) = 0.36 and P(A ∩ B) = 0.2

(i) P(A ∪ B) = P(A) + P(B) – P(A ∩ B) 

= 0.48 + 0.36 – 0.2 = 0.64. 

(ii) P (Getting only one award) 

= P(A) – P(A ∩ B) + P(B) – P(A ∩ B) 

= (0.48 – 0.2) + (0.36 – 0.2) 

= 0.28 + 0.16 = 0.44