Conditional Probability

A box contains four red balls and eight black balls. Two balls are randomly chosen from the box, and are not replaced. Let event B be choosing a black ball first and event R be choosing a red ball second. What are the following probabilities?

*8/12 *4/11 *8/33 *24

If events A and B are independent, what must be true?

P(A|B) = P(A)

Elias writes the numbers 1 through 20 on separate slips of paper. There are 16 white slips of paper and four yellow slips of paper. There are eight odd numbers on white slips, and the rest of the odd numbers are on yellow slips. Are the events "odd" and "yellow" independent?

yes, because the probability of choosing an odd number is equal to the probability of choosing an odd number given that the slip is yellow

The 154 tenth-graders at Wilson High School were polled on whether they enjoyed their algebra or geometry course more. The results are shown below. Algebra: 34 female, 33 male Geometry: 40 female, 47 male

*80/154 *47/87 *no, P (Male) does not equal P (Male I geometry)

Use the Venn diagram to calculate conditional probabilities. Which conditional probabilities are correct? Check all that apply.

*P(D | F) = 6/34 *P(E | D) = 7/25 *P(F | E) = 8/18

What statements are correct? Check all that apply.

*The conditional probability formula is P(X │ Y) = P (X U Y) / P (Y) *The notation P(R │ S) indicates the probability of event R, given that event S has already occurred. *Conditional probabilities can be calculated using a Venn diagram.

Lola pulls two marbles from a bag containing four red marbles, four blue marbles, and 12 yellow marbles without replacing them. What is the probability that she pulled out a red marble first and a yellow marble second? Express your answer in decimal form, rounded to the nearest hundredth.

0.13

A bag contains one red pen, four black pens, and three blue pens. Two pens are randomly chosen from the bag and are not replaced. To the nearest hundredth, what is the probability that a black pen is chosen first and then another black pen is chosen?

0.21

At Sanger's auto garage, three out of every five cars brought in for service need an oil change. Of the cars that need an oil change, four out of every seven also need a tire rotation. What is the probability that a car that comes into the garage needs both an oil change and a tire rotation? Give the answer in fraction form.

12/35

Seventy-five percent of the flowers in the arrangement are roses and the rest are tulips. Of the tulips, 50 percent are pink. To the nearest whole percent, what is the probability that a randomly chosen flower from the arrangement is a pink tulip?

13%

A study found that 23% of the cars manufactured last year were SUVs, 13% of the cars manufactured were white, and 2% of the cars manufactured were white SUVs. To the nearest whole percent, what is the probability that a car is an SUV, given that it is white?

15%

A dentist polls his patients and finds that 83 percent brush their teeth at least twice a day, 47 percent floss daily, and 19 percent brush at least twice a day and floss daily. What is the probability that a patient flosses daily, given that he or she brushes at least twice a day? Round to the nearest percent.

23%

Twenty-two percent of the large pieces of mail that Rachel received this week were magazines and the rest were catalogs. Of the catalogs, 36 percent were for clothing. To the nearest whole percent, what is the probability that a randomly chosen large piece of Rachel's mail was a clothing catalog?

28%

At a hospital, 56 percent of the babies born are boys. Of the baby girls born, 12 percent are premature. What is the probability of a premature baby girl being born at this hospital? Round to the nearest percent.

5%

Nadia's bookshelf contains 10 fiction books, two reference books, and five nonfiction books. What is the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book?

5/136

Lori downloaded all the pictures she took at Rita's wedding into a single computer folder. She took 86 of the 134 pictures with her camera and the remainder of them with her cell phone. Of the pictures Lori took with her cell phone, one out of every five was blurry. To the nearest whole percent, what is the probability that when she opens a random picture from the computer folder, it will be a blurry picture she took with her cell phone?

7%

At Mountain High School, the students were surveyed about their participation in band (B) and track (T). The results of the survey are shown in the Venn diagram. Given that a randomly chosen student participates in band, what is the probability that the student also participates in track?

9/33