probability.docx - 1 A box contains three marbles one red(R...

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1. A box contains three marbles, one red (R), one green (G), and one blue (B). A first marble is chosen, its color is recorded, and then it is replaced in the box and a second marble is chosen, and its color is recorded. Find the sample space. {(R, R), (R, G), (R, B), (G, R), (G, G), (G, B), (B, R), (B, G), (B, B)} {(R, G), (R, B), (G, R), (G, B), (B, R), (B, G)} {(R, B), (B, G), (G, R)} {R, G, B} Sample space => {(R,R), (R,G), (R,B), (G,R), (G,G), (G,B), (B,R), (B,B), (B,G)} i.e. 9 Sample space => not replaced => same color will not be there i.e. {(R,G), (R,B), (G,R), (G,B), (B,R), (B,G)} i.e. 6 2. If a committee of 3 is to be chosen at random from a class of 10 students, what is the probability of any particular committee being selected? (Enter your answer as a fraction.) Probability of an event, P ( E ) = n ( E ) n ( S ) n(S) = total number of outcomes in sample space S. n(S) = 10 C 3 = ( n! ) r! ( n r ) ! = 10 ! 3 ! ( 10 3 ) ! = 3628800 ( 30240 ) = 1 20 n(E) = number of outcomes in the event E = 1 P ( E ) = n ( E ) n ( S ) = 1 120 What if the committee is to consist of a president, a vice president, and a treasurer? (Enter your answer mc RN_1633648_1_0 {"js_version":0}
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as a fraction.) n(S) = 10 P 3 = n ( n 1 ) = 10 9 8 = 720 n(E) = 3! = 6 P ( E ) = n ( E ) n ( S ) = 6 720 = 1 120 3. In a town, 35% of the citizens contributed to the Republicans, 45% contributed to the Democrats, and 12% contributed to both. What percentage contributed to neither party?
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