you have 13 T-shirts in which 12 are not matching and 1 is matching.
at first attempt, you have to take non-matching t-shirt, probability = $\frac{12}{13}$
in second attempt, you have to take non-matching t-shirt, probability = $\frac{11}{12}$ ( due to you have 12 t-shirts only available with you )
in third attempt, you have to take non-matching t-shirt, probability = $\frac{10}{11}$ ( due to you have 11 t-shirts only available with you )
in fourth attempt, you have to take non-matching t-shirt, probability = $\frac{9}{10}$ ( due to you have 10 t-shirts only available with you )
in fifth attempt, you have to take non-matching t-shirt, probability = $\frac{8}{9}$ ( due to you have 9 t-shirts only available with you )
in sixth attempt, you have to take non-matching t-shirt, probability = $\frac{7}{8}$ ( due to you have 8 t-shirts only available with you )
in seventh attempt, you have to take non-matching t-shirt, probability = $\frac{6}{7}$ ( due to you have 7 t-shirts only available with you )
in eighth attempt, you have to take matching t-shirt, probability = $\frac{1}{6}$ ( due to you have 6 t-shirts only available with you )
Therefore total probability = $ \frac{12 * 11 * 10 * 9 * 8 * 7 * 6 * 1}{ 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 }$ = $ \frac{1}{ 13 }$