In: Statistics and Probability
Female students at a certain college participate in sports with the following probabilities: Soccer = 0.32 Basketball = 0.22 Tennis = 0.22 Both soccer and basketball = 0.06 All three sports = 0.03 Both soccer and tennis = 0.12 Both basketball and tennis = 0.05
a) Construct the associated Venn diagram with all probabilities
specified. (HINT: start with the idea that Pr(S ∩ B ∩ T) = 0.03 and
then work your way through the rest of the diagram). (SHOW WORK; 1
point)
Next, you select one female student at random for an interview;
determine the probability she plays
b) At least one of the three sports
c) Exactly one of the three sports
d) Exactly two of the three sports