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5. Let E and F be two events in an experiment. (a) Explain, using a Venn diagram, why (b) Explain why this implies that (c) Justify why E = (EnF)u(EnF") and P(E) = P(En F) + P(En Fª) P(F|E) P(E|F)P(F) P(E|F)P(F) + P(E|Fc)P(Fe) are equal by showing a computation that starts at P(FE) and ends at the term above, with each step a clear application of a formula or axiom we learned in class.

5. Let E and F be two events in an experiment. (a) Explain, using a Venn diagram, why (b) Explain why this implies that (c) Justify why E = (EnF)u(EnF") and P(E) = P(En F) + P(En Fª) P(F|E) P(E|F)P(F) P(E|F)P(F) + P(E|Fc)P(Fe) are equal by showing a computation that starts at P(FE) and ends at the term above, with each step a clear application of a formula or axiom we learned in class.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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No 5. a, b, c pls.

5. Let E and F be two events in an experiment. (a) Explain, using a Venn diagram, why (b) Explain why this implies that (c) Justify why E = (EnF)U(EnF") and P(E)=P(En F) + P(En Fe) P(FE) P(E|F)P(F) P(E|F)P(F) + P(E|Fe) P(Fe) are equal by showing a computation that starts at P(FE) and ends at the term above, with each step a clear application of a formula or axiom we learned in class. 2
Transcribed Image Text:5. Let E and F be two events in an experiment. (a) Explain, using a Venn diagram, why (b) Explain why this implies that (c) Justify why E = (EnF)U(EnF") and P(E)=P(En F) + P(En Fe) P(FE) P(E|F)P(F) P(E|F)P(F) + P(E|Fe) P(Fe) are equal by showing a computation that starts at P(FE) and ends at the term above, with each step a clear application of a formula or axiom we learned in class. 2
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