Question Type 1: Constructing Venn diagrams to calculate probabilities for 2 events Exercises

In a survey of 50 students, 20 study French, 15 study German, and 5 study both. Calculate the probability that a randomly chosen student studies neither language.

Two fair six-sided dice are rolled. What is the probability that their product is 12?

A fair coin is flipped. If it lands heads, a biased coin with $P(H)=0.75$ is tossed; if tails, the same biased coin has $P(H)=0.25$. What is the probability of getting heads on the second toss?

In a class of 80 pupils, 30 passed Maths, 50 passed English and 10 passed both. Find the probability that a randomly selected pupil passed at least one of the two subjects.

A person chooses Yes or No with equal probability. If they choose Yes, the next choice is Yes with probability 0.75; if they choose No, the next choice is Yes with probability 0.25. Find the probability that they choose Yes then No.

A factory uses machine A 60% of the time (defect rate 5%) and machine B 40% of the time (defect rate 2%). Calculate the probability that a randomly chosen item is defective.

In a community of 500 people, 200 own a car, 150 own a bicycle and 100 own both. Calculate the probability that a randomly chosen person owns neither.

A red die and a blue die are rolled. What is the probability that the red die shows a higher number than the blue die?

Given events A and B with $P(A)=0.7$, $P(B)=0.4$ and $P(A\cap B)=0.3$, find $P(A\cup B)$.

A delivery follows one of two routes: Route A with P=0.3 or Route B with P=0.7. On each route, on-time delivery occurs with probability 0.8 for A and 0.6 for B. If on time, customer satisfaction is 0.9; if late, satisfaction is 0.3. Find the probability of customer satisfaction.