10. The local Chamber of Commerce conducted a survey of 1,000 randomly selected shoppers at a mall. For all shoppers, gender of
shopper and items shopping for was recorded. The data collected is summarized in the following table:
Shopping For
Gender
Clothing
Shoes
Other
Total
Male
75
25
150
250
Female
350
230
170
750
Total
425
255
320
1,000
If a shopper is selected at random from this mall,
(a) What is the probability that the shopper is a female?
(b) What is the probability that the shopper is shopping for shoes?
(c) What is the probability that the shopper is a female shopping for shoes?
(d) What is the probability that the shopper is shopping for shoes given that the shopper is a female?
(e) Are the events \"female\" and \"shopping for shoes\" disjoint?
(f) Are the events \"female\" and \"shopping for shoes\" independent?