There are 52 cards in a standard deck of cards, with four suites: hearts, clubs, diamonds and spades. Each suit has 13 cards: Ace, \( 2,3,4,5,6,7,8,9,10 \), Jack, Queen, King . Let event \( A \) be choosing a card with 7 out of a standard deck of cards. Identify the numbers of each of the following. Enter the probability as a fraction: Provide your answer below: There are \( \square \) cards in the sample space. There are \( \square \) cards in event A. \( \mathrm{P}(\mathrm{A})=\square \), is the probability that you choose a 7 out of the deck of cards.

What is the probability of rolling a 1 or a 4 on a number cube labeled 1 through 6 ? B. \( \frac{1}{6} \) D. \( \frac{1}{3} \) E. \( \frac{1}{2} \) E. \( \frac{5}{6} \)

3. La probabilidad de que cierta clase de componente sobreviva a una prueba de choque es de 0.85. De los siguientes 15 componentes que se prueban calcule la probabilidad de que: a). sobrevivan 10 componentes. \( R=0.04489 \) b). no sobrevivan máximo 2 componentes. \( R=0.6042 \) c) calcule el promedio de componentes que sobreviven. \( R=12.75 \)

\( 1 \leftarrow \quad \begin{array}{l}\text { In a race in which five automobiles are entered and there are no ties, in how many ways can the } \\ \text { first three finishers come in? }\end{array} \)

In how many ways can the digits in the number \( 7,441,111 \) be arranged?

A club with fifteen members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?