B1. Consider events A, B and C, where A and B are mutually exclusive. Using multiple Venn diagrams, determine if the following proposition is correct, or not: (An B)U(ANC) = (An BenC)u(ANBNC).

6a. Supposed P(A) = .45, P(B) = .24, and events A and B are mutually exclusive. Find... a. P(A or B) =  b. P(B|A) = 6b. Supposed P(C) = .55, P(D) = .20, and events C and D are independent. Find... a. P(C and D) b. P(C or D) c. P(D|C) 6c. Suppose P(F) = .25, P(F or G) = .68, and events F and G are mutually exclusive. Find P(G)

The following is a two-way classification of 500 students based on gender: Male (M) or Female (F); and their student status: New (N), Continuing (C) or Re-entering (R). N C R Total M 60 170 70 300 F 40 110 50 200 Total 100 280 120 500 (a) Find the prob. that a r/s student is new. (b) Find the conditional prob. that a r/s student is new given that he is a male. (c) Are the two events “a r/s student is new” and “a r/s student is a male” independent? Why or why not?

A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below. Year in College Junior Freshman Sophomore Total Senior Foreign 15 65 100 25 205 Car Domestic 10 45 80 10 145 Total 25 110 180 35 350 The sophomore and domestic events are: Select one: O A. independent B. not mutually exclusive and independent O C. mutually exclusive and not independent O D. not mutually exclusive O E. None of the other answers O F. mutually exclusive

2. Which of the following shows the collection of all outcomes that are elements of one or the other of the sets A and B, or both of them? A. AUB B. An B C. P(An B) D. P(A U B)

4. The Venn diagram below shows the 12 students in Ms. Campbell's class. The diagram shows the memberships for the Tennis Club & the Softball Club. Note that Scott is outside the circles since he is not a member of either club. One student from the class is randomly selected. Scott Tennis Donna Tony Mai Reuben P(A) = P(B) = P(A or B) = P(A and B) = Softball Lashonda Let A denote the event "the student is in the Tennis Club" Let B denote the event "the student is in the Softball Club" Find the probabilities of the events below: Write each answer as a single fraction Tom Jenny Manuel Trey Laura Diane

Derive the simplest expressions for the following events

I. Let A, B and C be three events such that: A = (2, 4, 6, 8, 10, 12), B = (3, 6, 9, 12, 15) and C (1, 4, 7, 10, 13, 16). A. Illustrate using a Venn diagram B. Determine the elements of: 1. AUB= 2. AnB = 3. CNA= 4. CUA= 5. AnBnC=

A. Supply appropriate terms or phrases in the spaces below to form fact about events and its types. Experiment is any occasion in which the outcomes are These outcomes that may result in an experiment. And the collection of all now are the set of possible possible outcomes is called whose subset is called Events in an experiment can be classified into types. The first type of event is the simple event One example of this type of event is The second type of event is the compound event defined as which can be defined as One example of this is the This event can be further classified as and events depending on the chances of occurrences in events provided. Additionally, an event with sure occurrence is called while opposite to this is the When a pair of events are inclusive then these events can be identified as and one example of this is when

8.) If P(AorB) =0.7, P(A)=0.6, and P(AandB)=0.3, determine P(B)