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

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.

Among 120 people, 70 like tea, 50 like coffee, and 20 like both. Construct the Venn counts and find the probability that a randomly chosen person likes at least one beverage.

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

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

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 $P(A\cap B)$.

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

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 $P(A\cap B)$.

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