A drawer is filled with 2 black shirts , 7 white shirts, and 11 gray shirts. One shirt is chosen at random from the drawer. Find the probability that it is not a black shirt. Write your answer as a fraction in simplest form. square

To find the probability that a shirt chosen at random from the drawer is not a black shirt, we first need to determine the total number of shirts and the number of shirts that are not black.<br /><br />The total number of shirts is the sum of the number of black shirts, white shirts, and gray shirts:<br />\[<br />2 \text{ (black shirts)} + 7 \text{ (white shirts)} + 11 \text{ (gray shirts)} = 20 \text{ (total shirts)}<br />\]<br /><br />Next, we calculate the number of shirts that are not black. This is the sum of the number of white shirts and gray shirts:<br />\[<br />7 \text{ (white shirts)} + 11 \text{ (gray shirts)} = 18 \text{ (shirts that are not black)}<br />\]<br /><br />The probability that a randomly chosen shirt is not a black shirt is the ratio of the number of shirts that are not black to the total number of shirts:<br />\[<br />\frac{\text{Number of shirts that are not black}}{\text{Total number of shirts}} = \frac{18}{20}<br />\]<br /><br />To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 2:<br />\[<br />\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}<br />\]<br /><br />Thus, the probability that a randomly chosen shirt is not a black shirt is:<br />\[<br />\boxed{\frac{9}{10}}<br />\]