A survey was done asking how many students on campus enjoy c

A survey was done asking how many students on campus enjoy cardio and lifting weights. The survey found that 60% enjoyed lifting weights, 37% enjoy doing cardio, and 18% enjoy doing both.

1. What percentage of students do NOT enjoy lifting weights NOR enjoy doing cardio?

2. Are C and D mutually exclusive events? Why or why not?

3. Are the two events, C and D, independent? Explain, using probabilities.

4. If we know someone enjoys doing cardio, what is the probability they also enjoy lifting    weights?

Solution

1.) P(neither) = P((C u D)\') = 1 - P(C u D) = 1 - [P(C) + P(D) - P(C n D)]

= 1 - [0.6+0.37-0.18]

= 1 - 0.79

= 0.21

2.) Since P(C n D) = 0.18 , which is non zero, C and D are not mutually exclusive events

3.) P(C n D) = 0.18

P(C)*P(D) = 0.6*0.37 = 0.222

Since P(C n D) is not equal to P(C)*P(D), C and D are not independent events

4.) P(C|D) = P(C n D)/P(D) = 0.18/0.37 = 0.4865