Question

2. We are interested in analyzing data related to the Olympics from one decade. We are looking at individuals and if they participated in the summer or winter Olympics and whether or not they won a medal. Use S to denote summer and M to denote if a medal was won. The probability that someone participated in the summer Olympics is 72%. The probability that they won a medal is 13%. The probability that they won a medal and it was in the summer Olympics is 10%. a. What percentage of people participated in the summer Olympics or won a medal? b. What percentage of people participated in the winter Olympics? c. Given someone won a medal, what is the probability that they participated in the summer Olympics? d. What percentage of people did NOT participate in the summer games NOR won a medal? e. Are M and S mutually exclusive events? Why or why not? f. Are M and S independent events? Explain, using probabilities.

Answer 1

a)percentage of people participated in the summer Olympics or won a medal

=P(S u M)=P(S)+P(M)-P(S n M)=72+13-10 =75%

b) percentage of people participated in winter olympic=1-P(S)=100-72 =28%

c)

P(summer olympic|won medal)=P(S n M)/P(M)

=10/13=0.7692

d)

percentage of people did NOT participate in the summer games NOR won a medal

=100-P(S u M)=100-75 =25%

e)

as P(S n M) is not equal to 0 ; they are not mutually exclusive ;

as P(S n M) is not equal to P(S)*P(M); therefore S and M are not independent,