Five candidates {A. B, C, D, and E) have a chance to be selected to be on American Idol. Any subset of them (including none of them or all of them) can be selected, and assume that the selection process is completely random (the subsets of candidates are all equally likely). Find the probability of each of the following events. (a)

$$E_1$$

: "two candidates get selected." (b)

$$E_2$$

: "three candidates get selected." (c)

$$E_3$$

: "three candidates get selected, and A is not one of them."

Consider the sample space S={

$$o_1, o_2, o_3, o_4, o_5$$

}. Suppose that Pr(

$$o_1$$

=0.22 and Pr(

$$O_2$$

)=0.24. (a) Find the probability assignment for the probability space when

$$o_3, o_4$$

, and

$$o_5$$

all have the same probability. (b) Find the probability assignment for the probability space when

$$\operatorname { Pr } \left( o _ { 5 } \right) = 0.1$$

and

$$o_3$$

has the same probability as

$$o_4$$

and

$$o_5$$

combined.

There are 347 NCAA Division I college basketball teams. (a) How many different top-25 rankings are possible? [Assume that every team has a chance to be a top-25 team.] (b) How many ways are there to choose 64 teams (unseeded) to make it to the NCAA tournament? [ Assume every combination of 64 teams is possible.]

You are asked to give your answer using the notation

$$_ { n } P _ { r }$$

or

$$_ { n } C _ { i }$$

. You do not have to give an actual numerical answer, so you won't need a calculator. There are 10 athletes entered in an Olympic event. (a) In how many ways can one pick the winners of the gold, silver, and bronze medals? (b) In how many ways can one pick the seven athletes who will not earn any medals?

What are the different types of personnel needs assessments?

Determine the number of outcomes N in each sample space. (a) A student randomly answers a 10-question true-false quiz. The student's answer (T or F) to each question is observed. (b) A student randomly answers a 10-question multiple-choice quiz. The student's answer (A, B, C, D, or E) to each question is observed.

A computer password consists of four letters (A through Z) followed by a single digit (0 through 9). Assume that the passwords are not case sensitive (i.e., that an uppercase letter is the same as a lowercase letter). (a) How many different passwords are possible? (b) How many different passwords end in 1? (c) How many different passwords do not start with Z? (d) How many different passwords have no Z's in them?

How can the appropriate from of the adjective and the word in parenthesis be used to make a compliment? Modelo: casa / nuevo: ¡Qué nueva es la casa!

cuadros / interesante: ________________

An honest coin is tossed 10 times in a row. Find the probability of each of the following events. (a)

$$E_1$$

: "none of the tosses comes up tails." (b)

$$E_2$$

: "exactly one of the 10 tosses comes up tails." (c)

$$E_3$$

: "nine or more of the tosses come up tails."

Nine people (four men and five women) line up at a checkout stand in a grocery store. (a) In how many ways can they line up if all five women must be at the front of the line? (b) In how many ways can they line up if they must alternate woman, man, woman, man, and so on?

A set of reference books consists of eight volumes numbered through 8. (a) In how many ways can the eight books be arranged so that Volume 8 is in the correct position on the shelf (i.e., the last one from left to right)? (b) In how many ways can the eight books be arranged so that Volumes I and 2 are in their correct positions on the shelf?

A card is drawn at random out of a well-shuffled deck of 52 cards. Find the probability of each of the following events. (a)

$$E_1$$

: "draw a queen." (b)

$$E_2$$

: "draw a heart." (c)

$$E_3$$

: "draw a face card." (A "face" card is a jack, queen, or king.)

Nine people (four men and five women) line up at a checkout stand in a grocery store. (a) In how many ways can they line up? (b) In how many ways can they line up if the first person in line must be a woman?

A card is drawn from a well-shuffled deck of 52 cards . Find the probability of drawing a spade or a king.