Conditional Probabilities Answers

A random sample of adults was asked about their highest education level completed. The distribution of results is shown in the table.What is the probability that the highest level of education of an adult is a high school diploma, given that they have completed at least one of the education levels shown?

A researcher randomly sampled 222 high school students to determine their favorite color and whether or not they played a sport. The two-way table displays the data.A randomly selected student who participated in the survey is selected. Let event S = the student plays a sport and let event B = favorite color is blue, green, or purple. What is the value of P(B|S)?

A researcher randomly surveyed 122 college professors to determine what types of courses they teach and their sleeping habits. The two-way table displays the data.Suppose a survey respondent is randomly selected. Let M = professor teaches math and B = professor is an early bird. What is the value of P(B|M)?

A researcher randomly selects 95 high school swimmers and asks them which swim stroke is their strongest and which bathing suit brand they prefer, brand A or brand B. The two-way table displays the data. Suppose one of the students is randomly selected. Let B = the student prefers brand B and F = the student’s strongest stroke is freestyle.

A recent survey found that 65% of high school students were currently enrolled in a math class, 43% were currently enrolled in a science class, and 13% were enrolled in both a math and a science class. Suppose a high school student who is enrolled in a math class is selected at random. What is the probability that the student is also enrolled in a science class?

A researcher randomly selects 165 vehicles and sees how many miles each car has been driven and the color of the vehicle. The two-way table displays the data. Suppose a vehicle is randomly selected. Let M = the vehicle has been driven many miles and B = the vehicle is blue.

The following two-way table shows the distribution of high school students categorized by their grade level and book-type preference.

A researcher randomly selected 158 personal vehicles and noted the type of vehicle and its color. The two-way table displays the data.Suppose a vehicle is randomly selected. Let event C = convertible and R = red. What is the value of P(R|C)?

A department store’s survey suggests that 76% of shoppers buy food, 49% buy clothes, and 28% buy both food and clothes. Suppose a shopper is selected from the store at random and learn that they buy clothes. What is the probability that the shopper also buys food?

According to a recent survey of first-year high school students, 28% chew gum daily. The students were also asked if they had recently gotten a cavity filled at the dentist. Of the 47% of first-year students who responded that they had a cavity recently filled, only 39% chewed gum daily.Is chewing gum independent of having a cavity filled recently?