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

Among 120 people, 70 like tea, 50 like coffee, and 20 like both. Find the number of people who like only tea and the number of people who like only coffee. Hence, find the probability that a randomly chosen person likes at least one of these beverages.

In a survey of 100 students, 40 play football, 30 play basketball, and 10 play both. Construct the Venn diagram counts and find how many students play neither sport.

Given $P(A\cap B)=0.2$, $P(\text{neither } A \text{ nor } B)=0.1$, and $P(A)=0.6$, determine $P(B)$.

Given $P(A)=0.7$, $P(B)=0.4$, and $P(\text{neither }A\text{ nor }B)=0.1$, find $P(A\cap B)$.

In a standard 52-card deck, let $A$ be drawing a red card and $B$ be drawing a face card. Compute $P(A\cup B)$ and $P(A\cap B)$.

Out of 90 applicants, 60 passed exam A, 45 passed exam B, and 20 passed both. Find the probability that an applicant passed exactly one exam.

Given events $A$ and $B$ with $P(A)=0.6$, $P(B)=0.5$, and $P(A\cap B)=0.3$, find $P(\text{neither }A\text{ nor }B)$.

If $P(A\cup B)=0.8$, $P(A\cap B)=0.25$, and $P(A)=0.5$, find $P(B)$.

Given $P(A\cup B)=0.75$, $P(A)=0.45$, and $P(B)=0.60$, calculate $P(A\cap B)$.

Events $A$ and $B$ satisfy $P(A)=0.55$, $P(B)=0.65$, and $P(\text{exactly one of } A, B)=0.50$. Calculate $P(A\cap B)$.