4.3 Mutually and Non-Mutually Exclusive Events Assignment 1. Consider the Single Card Flip game. Copy and complete the table below to determine the number of ways each event can happen and the probability of each event occurring when a single card is drawn from a standard deck. Show your work where applicable. Give your probability answers as a fraction, decimal and percent. [16 In Words In Symbols In Symbols All red MA) : P(A) : All number n(B) = - P(B) : All cards n(S) = P(S) : Intersection: Both number and red n[A n B) = P[A F) B) = Only Red (red cards that are not number cards) MA) n(.4 n B) = PTA) P(A (I B) = Only Number {number cards that are not red cards) n(B) n(.l Fl B) = P(B) P(_.-], ['1 B) = Union: Red or Number n[A U B) = - PM U B) = Everything else MA U B)' = Phi U B)' = 2. A die is rolled. What is the probability that it shows a 3 or an even number? Use proper probability notation (as in the table above) to show how you got your answer. Is this an example of a mutually exclusive or non-mutually exclusive event? Justify your answer. [3 3. 0f the 175 grade 12 eLearning students, 58 have signed up for Biology, 53 have signed up for Chemistry, and 41 have signed up for Physics. The science students include 17 who are taking both Biology and Physics, 22 who are taking Biology and Chemistry, 21 who are taking Chemistry and Physics, and 10 who are taking all three science courses. a. Draw a Venn Diagram to represent this situation. [5 b. What is the probability that a randomly chosen student is not taking any science courses? Give your answer as a fraction, decimal and percent. [1 c. What is the probability that a randomly chosen student is taking only one science course? Give your answer as a fraction, decimal and percent. 2'2 d. What is the probability that a randomly chosen student is taking Biology or Chemistry? Give your answer as a fraction, decimal and percent. {3