SOLUTION: b) Probability distribution All customers of Amazonia purchase online. When buying, they provide customer details (include sex and age). The profile of Amazonia has been determin
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-> SOLUTION: b) Probability distribution All customers of Amazonia purchase online. When buying, they provide customer details (include sex and age). The profile of Amazonia has been determin
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Question 867615: b) Probability distribution All customers of Amazonia purchase online. When buying, they provide customer details (include sex and age). The profile of Amazonia has been determined as:
Age Under 20 20 – 40 40 – 60 Over 60
Male 10 60 20 25
Female 40 90 80 25
Total 50 150 100 50
(i) What is the probability that next customer order to be received will be from a male?
(ii) What is the probability that the next customer who orders is 40 years or older?
(iii) What is the probability that the next customer order received is from a female between 20 and 40?
(iv) Assuming that a customer only ever places one order. What is the probability that the 1st customer order received is from a female and the 2nd customer is a male?
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(i) What is the probability that next customer order to be received will be from a male?
There are 10+60+20+25 = 115 males total (add across the "male" row).
There are 40+90+80+25 = 235 females total (add across the "female" row).
There are 115+235 = 350 individuals total. Optionally, you can add up all the subtotals from the bottom of each column to get the same answer (50+150+100+50 = 350).
Now we use some of this info to answer the question:
There are 115 males total (see above).
This is out of 350 individuals total (see above).
So the probability is 115/350 = 23/70 = 0.32857142857142
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(ii) What is the probability that the next customer who orders is 40 years or older?
There are 100 people who are from 40 to 60 years of age (see the column that starts with "40-60" and look in the last row, which is the totals row).
There are 50 people who are over 60 years of age (see the column that starts with "over 60" and look in the last row, which is the totals row).
So there are 100+50 = 150 people ages 40 and up.
Divide this by the total 350 to get the probability
Probability: 150/350 = 3/7 = 0.42857142857142
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(iii) What is the probability that the next customer order received is from a female between 20 and 40?
Look at the cell in the "female" row and the "20 – 40" column. This value is 90. So there are 90 females who are 20 to 40 years old.
Divide this by the total 350 to get the probability
Probability: 90/350 = 9/35 = 0.25714285714286
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(iv) Assuming that a customer only ever places one order. What is the probability that the 1st customer order received is from a female and the 2nd customer is a male?
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