32 cars at a show 18 cars have four wheel drive, 21 are sports cars and 27 have four wheel drive or are sports cars

Question

Probability that a randomly selected car at the show is

a. Both four wheel drive and a sports car

b. Neither a four wheel drive nor a sports car

Answer 1

P(4WD) = 18/32

P(SC) = 21/32

P(4WD or SC) = 27/32

a)

P(4WD or SC) = P(4WD) + P(SC) - P(4WD and SC)

27/32 = 18/32 + 21/32 - P(4WD and SC)

-12/32 = - P(4WD and SC)

12/32 = P(4WD and SC)

b)

P( not (4WD or SC) ) = 1 - P(4WD or SC) = 1 - 27/32 = 5/32