a. Let A and B be two events such that P(A) = 0.05 and P(A U B) = 0,49. Calculate P(B') if events A and B are independent. ii) Calculate P(B) if P(A|B) = 0.32. iii) Suppose that a third event, C, exists. Derive an expression for finding P(B) in terms of P(C), P(B|C') and P(B U C'). Assume that events A and C are mutually exclusive.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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a. Let A and B be two events such that P(A) = 0.05 and P(A U B) = 0.49.
i)
Calculate P(B') if events A and B are independent.
ii)
Calculate P(B) if P(A|B) = 0.32.
iii)
Suppose that a third event, C, exists. Derive an expression for finding P(B) in terms of
P(C), P(B|C') and P(B U C'). Assume that events A and C are mutually exclusive.
Transcribed Image Text:a. Let A and B be two events such that P(A) = 0.05 and P(A U B) = 0.49. i) Calculate P(B') if events A and B are independent. ii) Calculate P(B) if P(A|B) = 0.32. iii) Suppose that a third event, C, exists. Derive an expression for finding P(B) in terms of P(C), P(B|C') and P(B U C'). Assume that events A and C are mutually exclusive.
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