In a survey that asked 69 people to indicate the reasons why they do not go to the gym, 44 responded that we’re too busy, 26 said they felt too/tired to go, and 12 said both.
(a) if a participant is randomly selected from the study, determine the probability that he/she does not go to the gym because he/she is too busy or because he/she is too tired/ lazy.
To find the probability that a participant does not go to the gym because they are too busy or because they are too tired/lazy, we need to sum the number of participants who responded that they were too busy and the number of participants who responded that they were too tired/lazy, and then subtract the number of participants who said both.
Number of participants who are too busy: 44
Number of participants who are too tired/lazy: 26
Number of participants who are both too busy and too tired/lazy: 12
Probability = (Number of participants who are too busy + Number of participants who are too tired/lazy - Number of participants who are both) / Total number of participants surveyed
Probability = (44 + 26 - 12) / 69
Probability = 58 / 69
Probability ≈ 0.841 or 84.1%