\begin{tabular}{l|l|}\hline 2. & \( \begin{array}{l}\text { En el siguiente caso: } \\ \text { Experimento aleatorio: Se gira una ruleta con secciones iguales enumeradas del } 1 \mathrm{al} 6 . \\ \text { Variable aleatoria } X: C \text { Cantidad de divisores del número que sale. } \\ \text { ¿Cuál es el recorrido? }\end{array} \) \\ \( \begin{array}{l}\text { a) } \operatorname{Rec} X:\{2,3,4,6\} \\ \text { b) } \operatorname{Rec} X:\{1,2,3,4\} \\ \text { c) } \operatorname{Rec} X:\{1,2,3,4,5,6\} \\ \text { d) } \operatorname{Rec} X:\{2,3,4\}\end{array} \) \\ \hline\end{tabular}

A bag contains 3 gold marbles, 9 silver marbles, and 21 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win \( \$ 4 \). If it is silver, you win \( \$ 2 \). If it is black, you lose \( \$ 1 \). What is your expected value if you play this game?

In parts (a) and (b) consider the following two events and then determine whether the events are independent or dependent. (a) Event 1: Owning a cat, Event 2: Planting a flower garden Independent Dependent (b) Event 1: One randomly selected student gets an A on the biology exam, Event 2: One randomly selected student gets selected to speak at graduation Independent Dependent

A box contains 3 red, 11 blue, and 9 green marbles. a) Two marbles are selected at random with replacement. Find the probability they are both red. b. Two marbles are selected at random without replacement. Find the probability that the first is blue and the second is green. c. Two marbles are selected at random without replacement. Find the probability that the first is blue and the second is yellow. Calculator

A certain game involves tossing 3 fair coins, and it pays \( 14 \ell \) for 3 heads, \( 5 \& \) for 2 heads, and \( 2 \& \) for 1 head. Is \( 5 \& \) a fair price to pay to play this game? That is, does the \( 5 \notin \) cost to play make the game fair? The \( 5 \& \) cost to play 1 a fair price to pay because the expected winnings are (Type an integer or a fraction. Simplify your answer.)

QUESTÃO 6: No lançamento simultâneo de dois dados a \( \begin{array}{llll}\text { probabilidade de se obter soma menor que } 8 \text { é? } \\ \begin{array}{llll}\text { a) } 5 / 36 & \text { b) } 1 / 12 & \text { c) } 7 / 12 & \text { d) } 5 / 18 \\ \text { e) } 5 / 12\end{array}\end{array} \)