In a group of 140 adults, 92 watch tennis, 81 play a sport and 40 do neither. find the probability that an adult chosen at random from those who watch tennis does not play a sport

Sure, let's solve this step by step.

Step 1:
First, let's figure out the total amount of people. The total number of adults is 140. From these adults, 40 do neither - they neither watch tennis nor do they play any sports.

Step 2:
In order to get the number of people who either watch tennis or play a sport (or both), we should subtract those, who do neither, from the total. So, total active adults (those who watch tennis or play a sport) would be;

Total active adults = Total adults - adults who do neither
= 140 - 40
= 100

Step 3:
The problem states that from this group, 92 watch tennis. Some of these might or might not be playing any sports, but we don't know that yet.

Step 4:
Out of the total active adults, 81 play a sport. The question asks about the probability of randomly picking someone, who watches tennis but does not play a sport.

Step 5:
For that, we need to figure out how many watch tennis AND play a sport. The number of adults who either watch tennis or play a sport or do both is 100, and separately there are 92 who watch tennis, and 81 who play a sport.

If we add those who watch tennis (92) and those who play a sport (81), we get 173. But we know that there are only 100 in total. That means that 173 - 100 = 73 adults are counted twice - they play a sport and watch tennis.

Step 6:
Therefore, the number of adults who just watch tennis but do not play a sport will be:

The number of adults who watch tennis - the number of adults who watch tennis AND play a sport = 92 - 73 = 19.

Step 7:
Now, to find the probability that an adult chosen at random from those who watch tennis does not play a sport, we just take the number of adults who just watch tennis (19) and divide it by the total number of individuals who watch tennis (92).

So, Probability = number of desired outcomes / total number of outcomes
= 19 / 92
= 0.2065 (rounded to four decimal places)

This means that if you randomly pick a person who watches tennis, there is approximately a 0.2065 or 20.65% chance that this person does not play a sport.

PROBABILITY =11/140 or 8% (approx.)