1. A company that sells three different products viz. Product A, Product B, and Product C conducted a survey to know which is the favorite product in the market. In total 500 samples were taken from four different regions viz. North, South, East, and the West.The responses are summarized in the following table.

North

South

East

West

Total

Product A

55

39

42

40

176

Product B

34

35

33

36

138

Product C

46

60

45

35

186

Total

135

134

120

111

500

With the help of the above table, identify the following probabilities

(a)Marginal probabilities for the three different products.

(b)Probability that the selected customer is from the East or West Region.

(c)Probability of selecting a customer from North who buys product B.

(d)Probability that the customer buys product C given that he/she is from the South Region.

(e)Probability that the customer is from the West region given that he/she buys product

(f)Probability that the customer is from the East region who buys product A.

(g) Probability that the customer buys product C given that he/she is from East Region