Question

2-146. + Disks of polycarbonate plasue nOll Jup analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: Shock Resistance High Low Scratch Resistance High Low 70 16 Let A denote the event that a disk has high shock resistance, d let B denote the event that a disk has high scratch resist- ance. Are events A and B independent? an

Answer 1

P(A) = (70 + 16) / 100 = 86 / 100 = 0.86

P(B) = (70 + 9) / 100 = 79 / 100 = 0.79

P(AB) = Probability of a disk has both high shock resistance and high scratch resistance = 70 / 100 = 0.70

P(A) x P(B) = 0.86 x 0.79 = 0.6794

Since P(AB) $\dpi{80} \neq$ P(A) x P(B), the events A and B are not independent.