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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.

Ask by Weaver Evans. in the United States
Mar 25,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The probability that the chosen shirt is not a black shirt is .

Solution

  1. First, find the total number of shirts in the drawer:
    • Black shirts: 2
    • White shirts: 7
    • Gray shirts: 11
    • Total shirts:
  2. Next, determine the number of shirts that are not black:
    • White shirts: 7
    • Gray shirts: 11
    • Total non-black shirts:
  3. The probability that a randomly chosen shirt is not black is the ratio of non-black shirts to the total number of shirts:
  4. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2:
Thus, the probability that the chosen shirt is not a black shirt is .

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

Mind Expander

To find the probability that a randomly chosen shirt is not a black shirt, we first need to determine the total number of shirts. There are 2 black shirts, 7 white shirts, and 11 gray shirts:
Total shirts = 2 (black) + 7 (white) + 11 (gray) = 20 shirts.
Next, we find the number of shirts that are not black. This includes the white and gray shirts:
Non-black shirts = 7 (white) + 11 (gray) = 18 shirts.
Now, we can calculate the probability of choosing a non-black shirt:
Probability(not black) = Number of non-black shirts / Total number of shirts = 18 / 20.
This fraction can be simplified:
18 / 20 = 9 / 10.
Thus, the probability that the chosen shirt is not a black shirt is .

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