A train is late with probability $\frac{1}{4}$ (misses appointment with probability $\frac{3}{5}$) and is on time with probability $\frac{3}{4}$ (misses appointment with probability $\frac{1}{5}$). Calculate the total probability that Minnie misses her dentist appointment.

A bag contains 3 red balls and 2 blue balls. Two balls are drawn at random one after another without replacement. Let $R_1$ be the event that the first ball is red and $R_2$ be the event that the second ball is red. Calculate $P(R_1\cap R_2)$.

Given that $P(B\mid A)=0.4$ and $P(B\mid A^{\prime })=0.4$, where $A^{\prime }$ is the complement of $A$, and $P(A)=0.7$, calculate the value of $P(B)$.

True or False: The general multiplication rule $P(A\cap B)=P(A)\times P(B\mid A)$ applies only if the events $A$ and $B$ are dependent.

For two events $A$ and $B$, $P(A)=0.6$, $P(B)=0.5$, and $P(A\cup B)=0.8$. Calculate the conditional probability $P(B\mid A)$.