et P(E) = 0.25, P(F) = 0.25, and P(E ∩ F) = 0.1. Draw a Venn diagram and find the conditional probabilities (a) P(F | E ∩ F) (b) P(EC | E )

Use the Venn diagram below to find the conditional probabilities.Maple Generated Plot(a) P(EC ∩ F | F) (b) P(E ∩ FC | F)0

Let event G = taking a math class. Let event H = taking a science class. Then, G ∩ H = taking a math class and a science class while G ∪ H = taking either a math class or a science class. Suppose P(G) = 0.42, P(H) = 0.45, and P(G ∪ H) = 0.25. What is P(G ∩ H)

Let P(E) 0.45, P(F) = 0.6, and P(Fn E) 0.3. Draw a Venn diagram and find the conditional probabilities. P(E | FC (a) P(F | EC) (b)

2b) Find zo for the following probabilities: i) P(Z > Zo) - 0.25 O-0.67 O o 0.67 O 0.5 Jimmy and Rosalynn Carter celebrate 76 years of marm to

Part 1: Suppose that F and X are events from a common sample space with P(F) # 0 and P(X) # 0. Prove that P(X) = P(X|F)P(F) + P(X|F)P(F). Hint: Explain why P(X|F)P(F) = P(Xn F) is another way of writing the definition of conditional probability, and then use that with the logic from the proof of Theorem 4.1.1. %3D Explain why P(F|X) = P(X|F)P(F)/P(X) is another way of stating Theorem 4.2.1 Bayes Theorem.