Question

5. In the Guelph fitness room, there are cardio machines, weight machines and free weights. The probability a user of a cardio machine is female is 0.9, the probability a user of a weight machine is female is 0.05, and the probability a user of free weights is female is 0.55. The probability a person would be on a cardio machine is 0.6, on a weight machine 0.3 and on a free weight is 0.1. Assume everyone is using one of the categories of equipment. Consider a random person in the Guelph fitness room. Find the probability that this person
(a) is not on a cardio machine;
(b) is using free weights or a weight machine;
(c) is male given that they are using free weights;
(d) is female given that they are using a weight machine;
(e) is using a weight machine and is female ;
(f) is using free weights and is male;
(g) is female;

Answer 1

a) Probability of a person on a cardio machine = 0.6

We need to find out the probability of a person not on a cardio machine = 1-0.6 = 0.4

Free weights = F , Cardio = c, Weight machines = W

b) Probability of using free weights and weight machine = P(F+W) = 0.3+0.1 = 0.4

c) Probability of a male using free weights = 1- Probability of a female using free weights = 1-.0.55 =0.45

d) Probabbility of a female given the person is using weight machine = 0.05/0.3 = 0.16666