When a survey of 800 people was done, 55% of those surveyed said they ate candy, 65% said they ate chips and 90% said they ate hot dogs. What is the smallest possible number of people who said they ate candy, chips and soda?
-Zach
To find the smallest possible number of people who said they ate candy, chips, and hot dogs, we need to consider the percentage that overlaps between the different categories.
First, let's calculate the number of people who said they ate candy.
55% of 800 people = (55/100) * 800 = 440 people said they ate candy.
Next, let's calculate the number of people who said they ate chips.
65% of 800 people = (65/100) * 800 = 520 people said they ate chips.
Finally, let's calculate the number of people who said they ate hot dogs.
90% of 800 people = (90/100) * 800 = 720 people said they ate hot dogs.
To find the smallest possible number of people who said they ate candy, chips, and hot dogs, we need to find the smallest overlapping value among these three categories.
Therefore, the smallest possible number of people who said they ate candy, chips, and hot dogs is 440, as this is the smallest overlapping value between the different categories.
To find the smallest possible number of people who said they ate candy, chips, and hot dogs, we need to determine how many people could possibly fall into all three categories.
First, we need to find the minimum number of people who said they ate candy, chips, and hot dogs individually. This can be done by multiplying the proportions by the total number of people surveyed.
The number of people who said they ate candy: 55% of 800 = 0.55 * 800 = 440
The number of people who said they ate chips: 65% of 800 = 0.65 * 800 = 520
The number of people who said they ate hot dogs: 90% of 800 = 0.90 * 800 = 720
Now we need to find the overlap between the three categories. Since we want the smallest possible number, we assume that all people who said they ate candy also said they ate chips and hot dogs.
Therefore, the smallest possible number of people who said they ate candy, chips, and hot dogs is equal to the number of people who said they ate candy: 440.
So, the smallest possible number of people who said they ate candy, chips, and hot dogs is 440.
The probability of all events occurring is found by multiplying the probabilities of the individual events.
.55 * .65 * .90 = ?