PROBLEM 4: PREFERENCE FOR CAN
(a) What is the probability of preferring a glass bottle?
b) What is the probability of preferring a glass bottle given that one lives in Region A?
c) What is the probability of preferring a can given that one lives in Region C or B?
Region A
Region B
Region C
Total
Prefer Can
100
150
140
Prefer Glass Bottle
200
180
200
Total
1)
2)
3)
a) The probability of preferring a glass bottle is the ratio of the number of people who prefer glass bottles to the total number of people surveyed. So, the probability is (200+180+200) / (100+150+140+200+180+200).
b) To find the probability of preferring a glass bottle given that one lives in Region A, we divide the number of people who prefer glass bottles in Region A by the total number of people living in Region A. So, the probability is 200 / (100+200).
c) To find the probability of preferring a can given that one lives in Region C or B, we add the number of people who prefer cans in Region C and Region B and then divide it by the total number of people living in Region C or B. So, the probability is (140+150) / (150+140+200+180).
To solve these probability questions, we need to use the information given in the table.
a) What is the probability of preferring a glass bottle?
To find this probability, we need to divide the number of people who prefer a glass bottle by the total number of people. Looking at the table, we can see that a total of 200 people prefer a glass bottle. We sum up the values for preferring a glass bottle in each region, which gives us 200 + 180 + 200 = 580. The total number of people is the sum of the values in the "Total" row for each region, which in this case is 1 + 2 + 3 = 6. The probability of preferring a glass bottle is therefore 580 divided by 6, which is 96.67%.
b) What is the probability of preferring a glass bottle given that one lives in Region A?
To find this probability, we need to look at the number of people who prefer a glass bottle in Region A and divide it by the total number of people in Region A. From the table, we can see that 200 people prefer a glass bottle in Region A. The total number of people in Region A is given as 1. So, the probability of preferring a glass bottle given that one lives in Region A is 200 divided by 1, which is 200%.
c) What is the probability of preferring a can given that one lives in Region C or B?
To find this probability, we need to look at the number of people who prefer a can in Region C or B and divide it by the total number of people in Region C or B. From the table, we can see that 140 people prefer a can in Region C and 150 people prefer a can in Region B. The total number of people in Region C or B is given by the sum of the values in the "Total" row for these two regions, which is 3. So, the probability of preferring a can given that one lives in Region C or B is (140 + 150) divided by 3, which is 96.67%.