Question

a coach asked her athletes if they enjoy running. fifty - five percent of the team do not like to run. of those, 60% enjoy cycling, while 70% of those who enjoy running also enjoy cycling. the tree diagram shows how the athletes are divided into subgroups. what is the total percentage of the athletes who do not enjoy cycling?
options: 22%, 70%, 13.5%, 35.5%

Explanation:

Step1: Find percentage not enjoying running

Total athletes as 100%. 55% do not enjoy running (since 100% - 45% = 55%? Wait, no: the problem says "Fifty - five percent of the team do not like to run" – so percentage not enjoying running is 55%, enjoying running is 100 - 55 = 45%.

Step2: Percentage not enjoying cycling from non - runners

Of non - runners (55%), 60% enjoy cycling, so 40% do not. So percentage: 55% 40% = 0.55 0.4 = 22%.

Step3: Percentage not enjoying cycling from runners

Of runners (45%), 70% enjoy cycling, so 30% do not. So percentage: 45% 30% = 0.45 0.3 = 13.5%.

Step4: Total percentage not enjoying cycling

Add the two percentages: 22%+13.5% = 35.5%? Wait, no, wait the options: wait, let's re - calculate. Wait, the problem says "Fifty - five percent of the team do not like to run" – so non - runners: 55%, runners: 45%.

For non - runners: 60% enjoy cycling, so 40% do not. So non - runners not enjoying cycling: 55% * 40% = 22%.

For runners: 70% enjoy cycling, so 30% do not. Runners not enjoying cycling: 45% * 30% = 13.5%.

Total not enjoying cycling: 22%+13.5% = 35.5%? But wait the options have 35.5% as one of them. Wait, but let's check again.

Wait, maybe I mixed up. Wait, the tree diagram: "Does not enjoy running" branch: then "Does not enjoy cycling" and "Enjoys cycling". "Enjoys running" branch: "Does not enjoy cycling" and "Enjoys cycling".

Given: 55% do not enjoy running (non - runners). Of non - runners, 60% enjoy cycling, so 40% do not: 55 * 0.4 = 22.

45% enjoy running (runners). Of runners, 70% enjoy cycling, so 30% do not: 45 * 0.3 = 13.5.

Total not enjoying cycling: 22 + 13.5 = 35.5%.

Answer:

35.5%