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In a group of 120 adults, 85 watch football, 78 play a sport and 20 do neither - OCR - GCSE Maths - Question 18 - 2017 - Paper 1
Question 18
In a group of 120 adults, 85 watch football, 78 play a sport and 20 do neither. Find the probability that an adult chosen at random from those who watch football do... show full transcript
Worked Solution & Example Answer:In a group of 120 adults, 85 watch football, 78 play a sport and 20 do neither - OCR - GCSE Maths - Question 18 - 2017 - Paper 1
Step 1
Calculate the number of adults who play a sport
Answer
To find the number of adults who watch football and play a sport, we can use the information that 20 adults do neither. Thus, the number of adults who either watch football or play a sport is: 120 - 20 = 100 adults.
Since 85 watch football, we denote the number of adults who both watch football and play a sport as x. Therefore, we have:
This simplifies to:
This means that 63 adults watch football and play a sport.
Step 2
Calculate the number of adults who watch football but do not play a sport
Answer
To find the number of adults who watch football but do not play a sport, we subtract the number of adults who both watch football and play a sport from the total number of adults who watch football:
Thus, 22 adults watch football and do not play a sport.
Step 3
Find the probability
Answer
The probability that an adult chosen at random from those who watch football does not play a sport is given by the ratio of the number of adults who watch football but do not play a sport to the total number of adults who watch football:
Calculating this gives:
Thus, the probability is approximately 0.2588.