Question

In the Zone 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 Zone. 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

	Cardio machine	Weight machine	Free weights	Total
Male	0.6-0.54 = 0.06	0.3-0.015 = 0.285	0.1-0.055 = 0.045	0.06+0.285+0.045 = 0.39
Female	0.6x0.90 = 0.54	0.3x0.05 = 0.015	0.1x0.55 = 0.055	0.54+0.015+0.055 = 0.61
Total	0.6	0.3	0.1	1

a) P(not on a cardio machine) = 1 - 0.6

= 0.4

b) P(using free weights or a weight machine) = 0.1 + 0.3

= 0.4

c) P(male | free weights) = 0.045/0.1

= 0.45

d) P(female | weight machine) = 0.05

e) P(weight machine and female) = 0.015

f) P(free weights and male) = 0.045

g) P(female) = 0.61