This exercise allows practice of the TREE DIAGRAMS useful in Conditional Probability computations. In this exercise, the tree diagram is constructed for events A, B, C, X, and Y.   (a) What is P(B)?  (b) What is P(X|B)?  (c) What is P(X AND B)?  (d) What is P(X)?  (e) What is P(B|X)?  (Please be sure to note this is NOT the same as P(X|B)) (IN THIS EXERCISE ALONE, ROUND YOUR FINAL ANSWER TO THREE DECIMAL PLACES) (f) Based on your computations, are events B and X independent events?

) Suppose that events A and B are independent. Show that p(A | B) + p(B)(1-p(A)) - P(A ∪ B) = 0.

Use the appropriate formula to answer the question: • Independent Probability: P(A and B) = P(A) x P(B) • Conditional Probability: P(A n B) = P(A) x P(B|A) • Addition Rule: P(A or B) = P(A) + P(B) – P(A and B) True or False: Events A and B are independent? P(A) = 0.60 P(B) = 0.70 P(A and B) = 0.42 True False

A student goes to the library. Let event A be that the student checks out a book and event B be that the student uses a library computer. Suppose that we happen to know that P (A) = 0.40, that P (B) = 0.30, and that P (B|A) = 0.5. Compute the following (1) P(Ac)(2) P(A AND B) (3) P(A|B)

For each set of probabilities, determine whether the events A and B are independent or dependent. (If necessary, consult a list of formulas.) Probabilities Independent Dependent = P(A 18) - 1 (a) P(A)=-;P(B) =;P(A\B) = 5 1 1 P(A) =;P (B) = P(A and B) = %3D 4 6. 1 1 P (B|A) = 1 (c) P(4)-극: P(B)-P(Bl4): %3D %3D 1 1 (d) P(A) = : P(B) = P(4 |B) = | %3D

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)

When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes.   What does P(M|B) represent? Is P(M|B) the same as P(BIM)?

A conditional Probability: P(A | B) is asking what is the probability we get event A if we know that event B occurred. A useful formula: P (A | B) = ||| P(A and B) P(B) Or: P(A | B) = (remaining # of ways to get A) / (remaining number of possible outcomes) A bag has 5 red balls, 7 green balls, and 8 purple balls. Two balls are going to be selected. After the first ball is drawn it is NOT returned to the bag. Find the probability the second is a red ball if you know the first chosen is a red ball. If A = event a red ball is selected: P(A|A) = ?