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Y and Z are independent, P(Y or Z) = 0.71 and P(Y) = 0.42. What is P(Z)?
AIt equals 0.29
BIt equals 0.71
CIt equals 0.42
DIt equals 0.50
Answer & Solution
Correct answer: D. It equals 0.50
1. Independence lets the joint probability be written as P(Y) times P(Z).
2. The addition rule then reads 0.71 equal to 0.42 plus P(Z) minus 0.42 times P(Z).
3. Collecting the P(Z) terms gives 0.71 minus 0.42 equal to 0.58 times P(Z).
4. The left side is 0.29.
5. Dividing 0.29 by 0.58 gives P(Z) equal to 0.50.
6. Answering 0.29 stops at the subtraction and forgets to divide by 0.58.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.3 Two Basic Rules of Probability_
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