Question Type 7: Given values of events, using diagrams to interpret probabilities Bootcamps

In a survey of 150 students, 90 study mathematics. What is the probability that a randomly selected student studies mathematics?

In the same survey of 150 students (90 study mathematics, 70 study physics, 30 study both), what is the probability that a student studies neither mathematics nor physics?

In a survey of 150 students, 90 study mathematics, 70 study physics, and 30 study both subjects. What is the probability that a randomly selected student studies mathematics or physics?

In a survey of 150 people, 90 like chocolate, 60 like vanilla, and 30 like both. What is the conditional probability that a person likes chocolate given that they like vanilla?

In a group of 100 students, 70 play soccer, 40 play basketball, and 25 play both sports. What is the probability that a randomly chosen student plays neither sport?

In a survey of 500 employees, 200 smoke, 300 drink alcohol, and 100 both smoke and drink. What is the probability that an employee smokes or drinks but not both?

In a class of 80 students, 50 take French, 30 take German, and 10 take both. What is the probability that a student takes German but not French?

In a class of 100 students, 60 study maths, 45 study science, and 35 study history. There are 25 who study both maths and science, 15 who study both maths and history, 10 who study both science and history, and 5 who study all three. What is the probability a randomly selected student studies at least one of these subjects?

In a sample of 250 people, 160 own a car, 120 own a bike, and 70 own both. Given that a person owns at least one of these, what is the probability they own both?

Two events A and B satisfy $P(A)=0.6$, $P(B)=0.5$, and $P(A\cap B)=0.3$. What is $P(A\Delta B)$, the probability that exactly one of A or B occurs?

Using the same class data (100 students, with counts as before), what is the probability that a randomly selected student studies exactly one of the three subjects?

Given three events A, B, C with $P(A)=0.4$, $P(B)=0.5$, $P(C)=0.3$, $P(A\cap B)=0.2$, $P(A\cap C)=0.15$, $P(B\cap C)=0.1$, and $P(A\cap B\cap C)=0.05$, find the probability that exactly two of the events occur.