If , what is the value of in terms of  and ?

The Conjunction Fallacy, where a person believes $P(A \& B)$ is more likely than $P(A)$ alone, is a violation of which basic probability law?

If and , what is the minimum possible probability for the conjunction ?

Given P(A)=0.6, P(B)=0.7, and P(A ∨ B)=0.88. Are outcomes A and B probabilistiically independent?

A system is composed of two independent modules, and  with probabilities of success and What is the probability that exactly one module will fail?

The probability of Bob passing his Physics exam is 0.70, the probability of his passing his English exam is 0.80, and the probability of his passing both 0.4. What is the probability that Bob passes Physics but not English?

Suppose P(A|B) = 0.6 and P(B) = 0.5. What is the probability of the conjunction P(A&B)?

A study finds $P(\text{Smoking})=0.2$, $P(\text{Lung Disease})=0.1$, and $P(\text{Smoking} \& \text{Lung Disease})=0.08$. Based on these probabilities, what is the conditional probability of getting lung disease given a person smokes?

Bob knows that his probability of passing his History exam is 0.70 and his probability of passing his English exam is 0.80. What is the highest probability that he can rationally assign to the proposition that he has passes at least one of the two exams?