Conditional Probability: assignment

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

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

A B D

At a hospital, 56 percent of the babies born are not girls. 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%

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? P(B)= P(R | B)= P(B n R)= The probability that the first ball chosen is black and the second ball chosen is red is about ______%

8/12 4/11 8/33 24%

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 Use the drop-down menus to answer the questions. What is the probability that a randomly chosen tenth-grader is male? What is the probability that a randomly chosen tenth-grader is male given that the tenth-grader prefers geometry? Are the events "male" and "geometry" independent?

80/154 47/87 no, p(male) does not equal p(male | geometry)

What statements are correct? Check all that apply.

A: The conditional probability formula is P(X │ Y) = p(x n y)/p(y) C: The notation P(R │ S) indicates the probability of event R, given that event S has already occurred. E: Conditional probabilities can be calculated using a Venn diagram.

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.

B: 23%

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?

B: 9/33

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