6 of the 10 integers between 1 and 10 inclusive are more than 4 (that is, 5,6,7,8,9,10).

The probability is the number of favorable outcomes divided by the number of possible outcomes: P(>4)=# of favorable outcomes/# of possible outcomes=\(\displaystyle\frac{{6}}{{10}}\)

5 of the 10 integers between 1 and 10 inclusive are odd (that is, 1,3,5,7,9). \(\displaystyle{P}{\left({o}{d}{d}\right)}=\frac{\text{of favorable outcomes}}{\text{of possible outcomes}}=\)\(\displaystyle\frac{{5}}{{10}}\)

3 of the 10 integers between 1 and 10 inclusive are move than 4 and odd (that is, 5,7,9). \(\displaystyle{P}{\left(>{4}{\quad\text{and}\quad}{o}{d}{d}\right)}\frac{\text{of favorable outcomes}}{\text{of possible outcomes}}=\)\(\displaystyle\frac{{3}}{{10}}\)

Use the General addition rule for any two events: \(\displaystyle{P}{\left({A}{U}{B}\right)}={P}{\left({A}\right)}+{P}{\left({B}\right)}-{P}{\left({A}⋂{B}\right)}\)

\(\displaystyle{P}{\left(>{4}{\quad\text{or}\quad}{o}{d}{d}\right)}={P}{\left(>{4}\right)}+{P}{\left({o}{d}{d}\right)}-{P}{\left(>{4}{\quad\text{and}\quad}{o}{d}{d}\right)}=\frac{6}{{10}}+\frac{5}{{10}}-\frac{3}{{10}}=\frac{{{6}+{5}-{3}}}{{10}}=\frac{8}{{10}}=\frac{4}{{5}}\)