Question 37 of 55intermediate🔧 ApplyFill in the Blanks3 marks
Fill in the blanks in 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
(i)
P(A) = 1/3, P(B) = 1/5, P(A ∩ B) = 1/15. Find P(A ∪ B).
Answer
7/15
(ii)
P(A) = 0.35, P(A ∩ B) = 0.25, P(A ∪ B) = 0.6. Find P(B).
Answer
0.50
(iii)
P(A) = 0.5, P(B) = 0.35, P(A ∪ B) = 0.7. Find P(A ∩ B).
Answer
0.15
Explanation
This question tests the application of the addition theorem of probability. The fundamental formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B) connects all four quantities. By rearranging this formula, we can find any missing value when three values are known. The textbook presents this formula in the context of probability of 'A or B' and 'A and B' events.