Conditional probability Quiz

1. $P(A)=0.5$, $P(B)=0.4$ and $P(A\cap B)=0.2$. Find $P(A|B)$.

• A. $0.1$
• B. $0.4$
• C. $0.5$
• D. $0.2$

2. $P(B)=0.6$ and $P(A|B)=0.5$. Find $P(A\cap B)$.

• A. $0.3$
• B. $1.1$
• C. $0.1$
• D. $0.5$

3. The probability of rain is $0.3$. If it rains the bus is late with probability $0.5$; if not, with probability $0.1$. Find $P(\text{late})$.

• A. $0.6$
• B. $0.15$
• C. $0.4$
• D. $0.22$

4. Using the same information, find the probability that it rained, given that the bus was late.

• A. $\frac{3}{10}$
• B. $\frac{15}{22}$
• C. $\frac{7}{22}$
• D. $\frac12$

5. What does $P(A|B)=P(A)$ show?

• A. $A$ and $B$ are mutually exclusive
• B. $A$ is certain
• C. $A$ and $B$ are independent
• D. $B$ is certain