$Given four pair of gloves, they are distributed to four persons.$

$Each person is given a right handed and left handed glove.$

$The probability that no person gets a pair is equal to$

 

$$\begin{gathered} \text{ The first distribution of 4 left gloves to four persons in 4! ways.} \\ \text{Now, no one gets the corresponding right glove=4!(1-}\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}) \\ =24(1-1+\frac{1}{2}-\frac{1}{6}+\frac{1}{24}) \\ =9 \end{gathered}$$

$Then, the number of favourable ways = 9·4!$

$Total number of ways =4!·4!$

$\therefore$Required Probability = $\frac{216}{4!·4!}=\frac{3}{8}=0.375$