Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find  $P(A \cap B)$

Given two independent events $A$ and $B$ such $P(A)=0.3,\, P(B)=0.6 .$ Find $P(A $ and not $B)$

In a horse race the odds in favour of three horses are $1:2 ,  1:3$ and $1:4$. The probability that one of the horse will win the race is

Two persons $A$ and $B$ throw a (fair)die (six-faced cube with faces numbered from $1$ to $6$ ) alternately, starting with $A$. The first person to get an outcome different from the previous one by the opponent wins. The probability that $B$ wins is

If the probability of a horse $A$ winning a race is $1/4$ and the probability of a horse $B$ winning the same race is $1/5$, then the probability that either of them will win the race is

Probability of solving specific problem independently by $A$ and $B$ are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that exactly one of them problem