A survey of one thousand people found that 70% of the people have a

CD player, 85% have a telephone, and 45.2% have a computer. At
least how many people have all three objects?

Is the answer 152?

To determine the number of people who have all three objects (CD player, telephone, and computer), we need to find the intersection of the three sets.

Let's start by finding the number of people who don't have a CD player, telephone, or computer. To do this, we calculate the complement of each set.

The complement of the CD player set is 100% - 70% = 30%.
The complement of the telephone set is 100% - 85% = 15%.
The complement of the computer set is 100% - 45.2% = 54.8%.

To find the number of people who don't have any of the three objects, we multiply the complements together:
30% * 15% * 54.8% = 2.61%.

Therefore, 2.61% of 1000 people don't have any of the objects, which is equal to 0.0261 * 1000 = 26.1 people.

Now, to find the number of people who have all three objects, we subtract the number of people who don't have any of the objects from the total number of people surveyed:
1000 - 26.1 = 973.9.

Since we cannot have a fraction of a person, we round down to the nearest whole number.

Therefore, at least 973 people have all three objects. So, the answer is not 152.

To determine the minimum number of people who have all three objects (CD player, telephone, and computer), we need to look for the highest percentage among the three objects.

In this case, the highest percentage is 85%, which represents the people who have a telephone. Therefore, we can use this percentage as a reference for the minimum number of people who have all three objects.

To calculate the minimum number of people who have all three objects, we multiply 85% by the total number of people (1000):

85% of 1000 = (85/100) * 1000 = 850

So, at least 850 people have a telephone. Since this is the highest percentage among the three objects, we can conclude that at least 850 people have all three objects (CD player, telephone, and computer).

Therefore, the answer is 850, not 152.