Final answer:
The probability that an adult chosen at random from those who watch tennis does not play a sport is approximately 20.7%.
Step-by-step explanation:
To find the probability that an adult chosen at random from those who watch tennis does not play a sport, we need to use the given information:
There is a group of 140 adults in total.
92 adults watch tennis.
81 adults play a sport.
40 adults do neither activity.
First, we determine the number of adults who watch tennis and play a sport, which can be done by subtracting those who do neither from the total:
140 - 40 = 100 adults who watch tennis or play a sport or both.
Now, the total number who watch tennis or play sports can also be written as a sum of those who only watch tennis, those who only play sports, and those who do both.
Let x be the number who do both. Then the equation is:
92 + 81 - x = 100
This simplifies to:
x = 92 + 81 - 100 = 73
Now we have 73 adults who both watch tennis and play sports. Therefore, the number of adults who watch tennis but do not play sports is:
92 - 73 = 19
The probability that an adult chosen at random from those who watch tennis does not play a sport is:
P = Number who watch tennis but don't play sports / Total who watch tennis
P = 19 / 92 = approximately 0.207 or 20.7%.