A survey of a groups viewing habits over the last year revea

A survey of a group\'s viewing habits over the last year revealed the following information: 28% watched basketball 29% watched baseball 22% watched soccer 14% watched basketball and baseball 20% watched basketball and soccer 8% watched baseball and soccer 6% watched all three sports. Calculate the percentage of the group that watched none of the three sports during the last year.

Solution

P( B) = 0.28, P(BB) = 0.29 , P(S) = 0.22

p( B & BB) = 0.14, P(B ans S) = 0.20 P(BB and S) = 0.08, P( B and BB and S) = 0.06

P( B U BB U S) = P(B)+P(BB) + P(S) - P( B & BB) - P(BB & S) - P(B & S) + P( B and BB and S) = 0.28+0.29+0.22-0.14-0.20-0.08+0.06 = 0.43

P( None watched t\\one of the three sports) = 1 - 0.43 = 0.57