Exam 5: Probability

We know, based on past history, that 72% of all students who enter a particular university as freshmen will graduate in four years.If graduation rates and gender are independent, what proportion of female freshmen would we expect to graduate in four years?

The California Lottery's Super Lotto Plus game involves picking five numbers between 1 and 47.There are 1,533,939 different ways that five numbers could be picked, and 571,341 different ways to pick at least one pair of consecutive numbers in this lottery game.What is the probability a person playing this game picks at least one pair of consecutive numbers?

Suppose we have a group of 5 children and wish to randomly select 2 from the group without replacement.How many possible unique samples of size 2 are possible if the order of selection does not matter?

An experiment consists of three tosses of a two-sided coin with the possible outcomes heads (H) or tails (T) from each toss.The outcome space is: ​ S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} ​ We define event A as "no heads are observed" and event B as "no tails are observed." What is AUB?

Suppose a population contains 1,000,000 people, 5000 of whom have a disease.The table shows the number of people who have the disease and test positive, etc. ​ ​ Based on the table, what is the probability that a person who tests positive actually has the disease?

All event probabilities (defined as P here) must be:

A computer security system requires a unique password for each user.The passwords use only letters of the English alphabet (26 possible letters) and cannot contain any repeats; that is, any given letter can be used only once in a password.If passwords have five letters each, how many passwords are available from which to choose?

Suppose you deal two cards from a standard deck of 52 cards.If you do not replace any cards between the deals, what is the probability you deal a king and then an even number (2, 4, 6, 8 or 10)?

Suppose you roll a pair of dice.What is the probability that you roll the two dice so that they add up to 7 or 11?

A recent demographic study conducted in the U.S.South classified all surveyed participants into one of only five possible religious categories: Roman Catholic, Protestant, Islamic, Jewish, Other.The table summarizes the survey results. ​ ​ Find P(Roman Catholic′).

Which of the following is equal to ?

A recent demographic study conducted in the U.S.South classified all surveyed participants into one of only five possible religious categories: Roman Catholic, Protestant, Islamic, Jewish, Other.The table summarizes the survey results. ​ ​ If the researchers designate Roman Catholic as R and Protestant as event Pr, what is P(RUPr)?

How many two-digit numbers are there, with both digits odd?

Sixty-five percent of the students who take introductory statistics start the semester with a poor opinion of statistics.If a randomly selected introductory statistics student has a poor opinion of statistics at the beginning of the semester, what is the probability that the person has had some negative experience with a previous math class?