In a group, there are $3$ men and $2$ women. Three persons are selected at random from this group. Find the probability that $1$ man and $2$ women or $2$ men and $1$ woman are selected.

[Correct the answer to one decimal place]

Out of $8$ points in a plane, $5$ are collinear. Find the probability that $3$ points selected at random will form a triangle.

[Correct the answer to two decimal place]

In a relay race, there are six teams $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F}$. What is the probability that $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ finish first, second, third and fourth respectively.

[Correct the answer to two decimal place]

In a relay race, there are six teams $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F}$. What is the probability that $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are first four to finish (in any order). Assume that all finishing orders are equally likely.

[Correct the answer to two decimal place]

Check whether the following probabilities $P\left(A\right)$ and $P\left(B\right)$ are consistently defined: 

$P\left(A\right)=0.5,P\left(B\right)=0.7$ and $P(A\cap B)=0.6$

Check whether the following probabilities $P\left(A\right)$ and $P\left(B\right)$ are consistently defined: 

$P\left(A\right)=0.5,P\left(B\right)=0.4$ and $P(A\cup B)=0.8$