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 258, because that's what I keep getting?

452 have a computer. That number could include at most 150 with no telephone, but probably fewer. So at least 302 have both computer and phone. The 300 with no CD player could be among that 302, but there are probably fewer. So at least 2 have all three. The most likely number having all three, if the distributions are uncorrelated, is 1000 x 0.452 x 0.7 x 0.85 = 269, but that is not what they ask for.

To find out the minimum number of people who have all three objects (CD player, telephone, and computer), we can use the concept of overlapping sets and the principle of inclusion-exclusion.

Step 1: Calculate the number of people who have at least one of the objects.
- From the given information, we know that 70% have a CD player, 85% have a telephone, and 45.2% have a computer.
- To calculate the number of people who have at least one of the objects, we need to sum up these percentages:
People with a CD player = 70% of 1000 = 0.70 * 1000 = 700 people
People with a telephone = 85% of 1000 = 0.85 * 1000 = 850 people
People with a computer = 45.2% of 1000 = 0.452 * 1000 = 452 people

Step 2: Use the principle of inclusion-exclusion to find the number of people who have all three objects.
- The principle of inclusion-exclusion states that to find the number of elements in the union of multiple sets, we need to sum the sizes of individual sets, subtract the sizes of pairwise intersections, add the size of the triple intersection, subtract the size of the quadruple intersection, and so on.
- In this case, we are looking for the size of the triple intersection (people who have all three objects).
- Using the principle of inclusion-exclusion, we can calculate the minimum number of people who have all three objects as follows:
Number of people who have all three objects = People with a CD player + People with a telephone + People with a computer
- (Pairs intersection) - (Pairs intersection) - (Pairs intersection)
+ (Triple intersection)

Substituting the values we calculated in Step 1:
Number of people who have all three objects = 700 + 850 + 452 - (Pairs intersection) - (Pairs intersection) - (Pairs intersection) + (Triple intersection)

Since the number of people who have all three objects is the minimum possible value, we can assume there is no intersection among pairs of objects and calculate the triple intersection:
Number of people who have all three objects = 700 + 850 + 452 - 0 - 0 - 0 + (Triple intersection)
= 2002 + (Triple intersection)

Therefore, the answer is 2002 or more. We cannot determine the exact number without additional information about the intersections. So, the answer you mentioned (258) is not correct.