49. The accompanying table gives information on the type of coffee selected by s

Question

49. The accompanying table gives information on the type of coffee selected by someone purchasing a single cup at a par- ticular airport kiosk Sma Medium Regular ecaf 14% 20% 20% 10% arge 26% 10% Consider randomly selecting such a coffee purchaser a. What is the probability that the individual purchased a small cup? A cup of decaf coffee? b. If we learn that the selected individual purchased a small cup, what now is the probability that he/she chose decaf coffee, and how would you interpret this probability? c. If we learn that the selected individual purchased decaf what now is the probability that a sma size was selected, and how does this compare to the correspon- ding unconditional probability of (a)?

Explanation / Answer

here from above data:

a) probability that individual purchase a small cup =0.34

probability that individual purchase a decaf coffeee =0.4

b)

P(decaf|small cup) =0.2/0.34 =0.5882

we interpret that 58.52% of people with small cup choses decaf coffee,

c)

P(small cup|decaf) =0.2/0.4 =0.5

this is hihger than part a) which means that people with decaf coffee choice are more prone to purchase small cup than general population,

small medium large total regular 0.14 0.2 0.26 0.6 decaf 0.2 0.1 0.1 0.4 total 0.34 0.3 0.36 1

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