The accompanying table gives information on the type of coffee selecte

ZIHLOLEp3

ZIHLOLEp3

Answered question

2021-11-15

The accompanying table gives information on the type of coffee selected by someone purchasing a single cup at a particular airport.
Small Medium Large
Regular Coffee 14% 20% 26%
Black Coffee 20% 10% 10%
Consider randomly selecting such a coffee purchaser.
a. What is the probability that the individual purchased a small cup?
b. What is the probability that the individual purchased a cup of black coffee?
c. If we learn that the selected individual purchased a small cup, what now is the probability that he/she chose black coffee, and how would you interpret this probability?
d. If we learn that the selected individual purchased black coffee, what now is the probability that a small size was selected?

Answer & Explanation

Eprint

Eprint

Beginner2021-11-16Added 13 answers

Step 1
a) From the table, we can see that a total of 14%+20%=34% of people purchased a small cup of coffee.
So, the probability that the individual purchased a small cup is 34% or 0.34
Answer(a): 34% or 0.34
Step 2
b) From the table, we can see that a total of 20%+10%+10%=40% of people purchased a black coffee.
So, the probability that the individual purchased a cup of black coffee is 40% or 0.40
Answer(b): 40% or 0.40
Step 3
c) We have to use conditional probability.
Interpretation: Probability of the person having black coffee, given he orders a small cup of coffee.
P(black coffee | small cup)
=P(black coffee and small cup)P(small cup
=20%14%+20%
=2034
=1017
Answer(c): 1017
Step 4
d) We have to use conditional probability
Interpretation: Probability of the person having a small cup of coffee, given he orders a black coffee.
P(small cup|black coffee)
=P(small cup and black coffeeP(black coffe)
=20%20%+10%+10%
=2040
=12
Answer(d): 12

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