60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation – e.g.,

Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a club. Are these events independent? Input Yes or No:  Determine the probability of drawing a diamond and then a club  without  replacement.   Write your answer in decimal form, rounded to four decimal places as needed. Answer =  Linda draws a diamond from a standard deck of 52 cards. She returns the diamond to the deck, then draws a second card. Her second card is a club. Are these events independent? Input Yes or No:  Determine the probability of drawing a diamond and then a club  with  replacement.   Write your answer in decimal form, rounded to four decimal places as needed. Answer =

Given P(A) = 0.2, P(B) = 0.6 and P(A and B) = 0.08. Explain how you know events A and B cannot be mutually exclusive.