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Female students at a certain college participate in sports with the following probabilities: Soccer = 0.32...

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Statistics

Female students at a certain college participate in sports withthe following probabilities: Soccer = 0.32 Basketball = 0.22 Tennis= 0.22 Both soccer and basketball = 0.06 All three sports = 0.03Both soccer and tennis = 0.12 Both basketball and tennis = 0.05

a) Construct the associated Venn diagram with all probabilitiesspecified. (HINT: start with the idea that Pr(S ∩ B ∩ T) = 0.03 andthen work your way through the rest of the diagram). (SHOW WORK; 1point)
Next, you select one female student at random for an interview;determine the probability she plays

  1. b) At least one of the three sports

  2. c) Exactly one of the three sports

  3. d) Exactly two of the three sports

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