A store sells two different brands of dishwasher soap, and each brand comes in three different sizes: small (S), medium (M), and large (L). The proportions of the two brands and of the three sizes purchased are displayed as marginal totals in the following table. P1E2 0 not E1 P1E 2 2 0E1 2 EC 1 322 Chapter 6 Probability Bold exercises answered in back Data set available online but not required Video solution available Suppose that any event involving brand is independent of any event involving size. What is the probability of the event that a randomly selected purchaser buys the small size of Brand B1 (the event )? What are the probabilities of the other brandsize combinations?

3.1 Ans12) (a) Mean = Sum of all values divided by the number of values. Mean = ∑ x /n = 23/5 = 4.6 In order to calculate the median, we arrange the set of numbers in increasing order: 2 2 3 6 10. As the number of observations are odd, therefore median is the third value which is 3. Median = 3. Mode is the number that occurs most frequently in the given data. In this case, 2 occurs most frequently. So, mode is 2. (b)As per the question, we add 5 to each of the data values. New data set: 7 7 8 11 15. Mean = ∑ x /n = 48/5 = 9.6 In order to calculate the median, we arrange the set of numbers in increasing order: 7 7 8 11 15. As the number of observations are odd, median is the middle value which is the third value in this case. Median = 8. Mode is the number that occurs mos