multiplication rule for dependent events

There are 36 students on the debate team at a school. There are 6 seniors, 12 juniors,10 sophomores, and 8 freshmen on the team. The coach is going to select 4 students at random to participate in the next debate. Calculate the probability that all 4 students are sophomores.

0.0036

Many of the students at a school play sports: 17% of students play soccer, 23% play football, and 48% of the football players play soccer. What is the probability that a randomly selected student plays both?

0.1104

This year the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot, 20% still got the flu. Of those who did not receive the flu shot, 65% got the flu. Use the tree diagram to determine the probability that a person with the flu is a person who received a flu shot. Enter your answer as a decimal to the ten thousandths place.

0.1165

What is the probability that a student took AP Chemistry, given they did not get into their first-choice college? Enter your answer as a decimal to the ten thousandths place.

0.2273

The probability that a student passes the AP Stats exam is 0.57. The probability that a student passes the AP Calculus exam is 0.43. The probability that a student passes the AP Stats exam given they passed the AP Calculus exam is 0.85. Find the probability that a student passes both exams.

0.3655

This year the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot, 20% still got the flu. Of those who did not receive the flu shot, 65% got the flu. What's the probability that a randomly selected adult got the flu? Enter your answer as a decimal to the ten thousandths place.

0.5150

Students must take an AP Sciences exam their senior year: 25% take AP Chemistry, 35% take AP Physics, 30% take AP Environmental Science, and the remaining seniors take AP Biology. Of those who take AP Chemistry, 45% get accepted to their first-choice college, compared with 55% who take AP Physics, 20% who take AP Environmental Science, and 30% who take AP Biology. Use the tree diagram to determine the probability that a student did not get into their first-choice college. Enter your answer as a decimal to the ten thousandths place.

0.6050

Students must take an AP Sciences exam their senior year: 25% take AP Chemistry, 35% take AP Physics, 30% take AP Environmental Science and the remaining seniors take AP Biology. Of those who take AP Chemistry, 45% get accepted to their first-choice college, compared with 55% who take AP Physics, 20% who take AP Environmental Science, and 30% who take AP Biology. Use the partially completed tree diagram to fill in the indicated labels.

environment science 0.10 1st choice 0.45 0.55

This year, the CDC reported that 30% of adults received their flu shot. Of those adults who received their flu shot, 20% still got the flu. Of those who did not receive the flu shot, 65% got the flu. A partially completed tree diagram is shown. Fill in the indicated labels.

flu shot flu no flu 0.30 0.20