Exam 7: Probability

Use the following information for questions: A student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years. -What is the probability that the study used randomization, if we already know that the study was a retrospective observational study?

Use the following information for questions: Suppose two different states each pick a two-digit lottery number between 00 and 99 (for a 100 possible numbers). -What is the probability that both states pick the same number?

A test to detect prostate cancer in men has a sensitivity of 95%. This means that

Use the following information for questions: In the Banana Republic there are two producers of PCs, referred to as Pac and Bell. Assume that there are no PC imports. The market shares for these two producers are 70% for Pac and 30% for Bell. One executive at Bell proposes a longer warranty period (similar to one given by auto makers) to be offered at a slight extra cost as a plan to increase market share. A market research company appointed by Bell conducts a census of PC owners on their opinion of this warranty proposal. Among owners of a PC made by Pac, 50% like the proposal, 30% are indifferent to it, while the remaining owners oppose it. Among owners of a PC made by Bell, 70% like the proposal, 20% are indifferent to it, and the remaining owners oppose it. -A PC owner will be selected at random. What is the probability that the owner will be opposed to the proposal of a new warranty at extra cost?

Use the following information for questions: Students who live in the dorms at a college get free T.V. service in their rooms, but only receive 6 stations. On a certain evening, a student wants to watch T.V. and the six stations are broadcasting separate shows on baseball, football, basketball, local news, national news, and international news. The student is too tired to check which channels the shows are playing on, so the student picks a channel at random. -The two events F = {the student watches football} and A = {the student watches an athletic event} are

Use the following information for questions: A standard 52-card deck is shuffled and 5 cards are picked from the top of the deck. -The probability that the first four cards are a red suit (Heart or Diamond) and the last card is a black suit (Spade or Club) is

Suppose that the probability of event A is 0.2 and the probability of event B is 0.4. Also, suppose that the two events are independent. Then P(A|B) is:

The lifetime risk for a woman to develop breast cancer is estimated to be about 1 in 8. Express this probability as a fraction, as a proportion, and as a percentage.

Use the following information for questions: A mail-order company classifies its customers by gender (male/female) and by location of residence (urban/suburban). The market research department has determined that 2/3 of their customers are female and that 75% of their customers live in the suburbs. They have also determined that gender and location of residence seem to be independent of one another. -Making up the majority of their customers, the females and suburban customers are identified as the focus group for their new ad campaign. If the mail order company will randomly select one of their customers, what is the probability that it will be a suburban customer or a female?

When a fair coin is tossed two times, there is a 25% chance of getting 0 heads and a 50% chance of getting 1 head. What is the chance of getting 2 heads?

Use the following information for questions: For each of the following statements, determine if they are true or false. -If events A and B are known to be independent and P(A) = 0.2 and P(B) = 0.3, then P(A and B) = 0.5.

Use the following information for questions: A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and one male assistant (Josh). Each TA teaches one discussion section. -A student picks a discussion section. The two events W = {the TA is a woman} and M = {the TA is a man} are

Use the following information for questions: A card is drawn at random from a standard 52-card deck. -The conditional probability that the card is a King given that a face card (Jack, Queen, or King) was drawn is

Consider the following three descriptions of outcomes after tossing 6 coins: {all six heads}, {3 heads and 3 tails (in any order)}, and {4 heads and 2 tails (in any order)}. Which of the following represents the ordering of these three descriptions in order of highest to lowest probability?

Use the following information for questions: Students who live in the dorms at a college get free T.V. service in their rooms, but only receive 6 stations. On a certain evening, a student wants to watch T.V. and the six stations are broadcasting separate shows on baseball, football, basketball, local news, national news, and international news. The student is too tired to check which channels the shows are playing on, so the student picks a channel at random. -The events F = {the student watches football} and B = {the student watches baseball} are

Use the following information for questions: A study was conducted at a small college on first-year students living on campus. A number of variables were measured. The table below provides information regarding number of roommates and end of term health status for the first-year students at this college. Health status for individuals is measured as poor, average, and exceptional. -Are the events H = {the student has poor health status} and N = {the student has no roommates} independent?

Use the following information for questions: A standard 52-card deck is shuffled and 5 cards are picked from the top of the deck. -The probability that the first four cards are Aces and the last card is a 2 is

Use the following information for questions: Students who live in the dorms at a college get free T.V. service in their rooms, but only receive 6 stations. On a certain evening, a student wants to watch T.V. and the six stations are broadcasting separate shows on baseball, football, basketball, local news, national news, and international news. The student is too tired to check which channels the shows are playing on, so the student picks a channel at random. -On a different night, two students who don't know each other each choose a channel this way. The two events, N = {the first student watches a news broadcast } and F = {the second student watches football} are

When two cards are drawn at random from a 52 card deck, the probability of drawing one Jack is 0.145. The probability of drawing one Ace is 0.145, and the probability of drawing a Jack and an Ace is 0.012. What is the probability of drawing a Jack or an Ace?

If one card is randomly picked from a standard deck of 52 cards, the probability that the card will be a number from 2 through 10, or a Heart, or both, is