Answer to Question #186298 in Statistics and Probability for Aliyajaved

Question

c) A quality-control manager found that 30% of work related problems occurred on Mondays and that 20% occurred in the last hour of a day’s shift. It was also found that 4% of worker-related problems occurred in the last hour of Monday’s shift I. Are the events “problem occurs on Monday” and“ problem occurs in the last hour of the day’s shift” statistically independent? II. What is the probability that a work-related problem occur on any day other then the start of the business week (assume that the Monday’s probability of work-related problem is generalizable for other days of the week), or a work-related problem doesn’t occur on the last hour of Monday’s shift? Assume that the two conditions, given in this part, are independent.  

Answer 1

P( Monday)$=P(M)=0.3$

P(Last hour)$=P(L)=0.2$

P(Monday and Last hour)$=P(M\cap L)=0.04$

(a) $P\bar{(\dfrac{L}{M})}=1-P(\dfrac{L}{M})=1-\dfrac{P\cap M}{P(M)}=1-\dfrac{0.04}{0.3}=1-0.133=0.867$

(b) $P(M)\times P(L)=(0.3)(0.2)=0.06\neq 0.04$

Hence The two conditions are not independent.