Probability preguntas y respuestas

A marble is selected from a bag containing eight marbles numbered 1 to 8 . The number on the marble selected will be recorded as the outcome. Consider the following events. Event \( A \) : The marble selected has an even number. Event \( B \) : The marble selected has a number greater than 3 . Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas. (a) Event " \( A \) or \( B ":\{2,4,5,6,7,8\} \) (b) Event " \( A \) and \( B ":\{4,6,8\} \) (c) The complement of the event \( A:\{D\} \)

A marble is selected from a bag containing eight marbles numbered 1 to 8 . The number on the marble selected will be recorded as the outcome. Consider the following events. Event \( A \) : The marble selected has an even number. Event \( B \) : The marble selected has a number greater than 3 . Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas. (a) Event " \( A \) or \( B^{n}:\{\mathbb{T}\} \) (b) Event " \( A \) and \( B^{n}:\{\mathbb{T}\} \)

Jina has a bag with 8 balls numbered 1 through 8 . She is playing a game of chance. This game is this: Jina chooses one ball from the bag at random. She wins \( \$ 1 \) if the number 1 is selected, \( \$ 2 \) if the number 2 is selected, \( \$ 5 \) if the number 3 is selected, \( \$ 6 \) if the number 4 is selected, \( \$ 8 \) if the number 5 is selected, \( \$ 10 \) if the number 6 is selected. She loses \( \$ 14 \) if 7 or 8 is selected. (a) Find the expected value of playing the game. dollars (b) What can Jina expect in the long run, after playing the game many times? (She replaces the ball in the bag each time.) She can expect to win \( \square \) dollars per selection. She can expect to lose money. Oina can expect to break even (neither gain nor lose money).

There are 7 acts in a talent show. An acrobat, a comedian, a guitarist, a pianist, a singer, a violinist, and a whistler. A talent show host randomly schedules the 7 acts. Compute the probability of each of the following events. Event A : The whistler is first, the pianist is second, the acrobat is third, and the guitarist is fourth. Event B: The first four acts are the comedian, the pianist, the guitarist, and the acrobat, in any order. \( P(A)=\square \) \( P(B)=\square \)

Suppose we want to choose 4 colors, without replacement, from 16 distinct colors. (a) How many ways can this be done, if the order of the choices is relevant? (b) How many ways can this be done, if the order of the choices is not relevant? (

\( \begin{array}{l}\text { Pentaksiran Akhir Tahun } \\ 10 \text { Sebuah kotak mengandungi } 8 \text { batang pen biru dan } 4 \text { batang pen merah. Dua batang pen dikeluarkan secara rawak tanpa } \\ \text { pengembalian. } \\ \text { A box contain } 8 \text { blue pens and } 4 \text { redpens. Two pens are drawn at random from the box, without replacement. } \\ \text { (a) Hitung kebarangkalian bahawa kedua-dua pen yang dikeluarkanadalah sama wama. } \\ \text { Calculate the probability that both pensdrawn are the same colour. }\end{array} \) [2 markah] \( ] \)

\begin{tabular}{l} Evaluate. \\ \( \qquad \)\begin{tabular}{|c|c|}\( \frac{4!5!}{3!7!} \) \\ Simplify your answer as much as possible. \\ \begin{tabular}{|c|}\hline\( \square \) \\ \( \square \)\end{tabular} \\ \hline\end{tabular} \\ \hline\end{tabular}

(b) Subtract. (c) Select the answer that makes the sentence true. \( 1-P(X) \) is the same as \( P(\operatorname{not} X) \)

5) Se lamza una mónecia y un dado al mismó tiempo aldcuales y cuantos elemenios tienen ol espocio muestral

24.-Para hacer un color especifico de pintura se utilizan 5 colores distintos. Al inicio se mezclan 2 colores sin importar el orden. ¿Cuántas formas distintas existen para elegir los 2 colores? A) 20 B) 10 C) 25 D) 40