Since the events are mutually exclusive, we can write
[tex]P(\text{red striped}\cap jean\text{ shorts)=P(red striped)}\times P(jean\text{ shorts)}[/tex]
the probability to select the red striped shirt is
[tex]P(\text{red striped)=}\frac{1}{5}[/tex]
because there are 5 choices. In the same way, the probability to select the jean shorts is
[tex]P(\text{jean shorts)=}\frac{1}{3}[/tex]
because there are 3 choices. Then, by substituting these results into our first equation, we get
[tex]\begin{gathered} P(\text{red striped}\cap jean\text{ shorts)=}\frac{1}{5}\times\frac{1}{3} \\ P(\text{red striped}\cap jean\text{ shorts)=}\frac{1}{15} \end{gathered}[/tex]
that is, 1/15
