Question
Question: A, B, C are events such that P (1) = 0.3, P (2) = 0.4, P (3) = 0.8, P (A Ē B) = 0.08, P(AĒC) = 0.28,...
A, B, C are events such that P (1) = 0.3, P (2) = 0.4, P (3) = 0.8, P (A Ē B) = 0.08, P(AĒC) = 0.28, P (A Ē B Ē C) = 0.09. If P (A Č B Č C) 0.75, then P (B Ē C) lies in the interval -
A
(0.23, 0.48)
B
(0.2, 0.4)
C
(0.25, 0.50)
D
None
Answer
(0.23, 0.48)
Explanation
Solution
We know that the probability of occurrence of an event is always less than or equal to 1 and it is given that
P (A Č B Č C) ³ 0.75
\ 0.75 £ P (A Č B Č C) £ 1 Ž 0.75 £ P (1) + P (2) + P (3) – P (A Ē B) – (B Ē C) – P (A Ē C) + P (A Ē B Ē C) £ 1
Ž 0.75 £ 0.3 + 0.4 + 0.8 – 0.08 – P (B Ē C) – 0.28 + 0.09 £ 1 Ž 0.75 £ 1.59 – 0.36 – P (B Ē C) £ 1 Ž 0.75 £ 1.23 – P (B Ē C) £ 1 Ž – 0.48 £ – P (B Ē C) £ – 0.23
Ž 0.23 £ P (B Ē C) £ 0.48. Hence (1) is correct answer