In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. What is the probability that a person chosen at random likes both coffee and tea?
Probability= #of favorable cases
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# total possible
42+27=69
This question is not accurate.
60-27=33
To find the probability that a person chosen at random likes both coffee and tea, we first need to determine the number of people who like both drinks.
We are given that 27 people like cold drinks, 42 people like hot drinks, and each person likes at least one of the two drinks. Since the total number of people in the group is 60, and everyone likes at least one drink, we can add the number of people who like cold drinks (27) to the number of people who like hot drinks (42).
27 + 42 = 69
However, this sum counts the number of people who like either cold drinks or hot drinks, without considering those who like both. Therefore, to find the number of people who like both coffee and tea, we need to subtract the number of people who like either cold or hot drinks but not both.
Let's define the following sets:
- A: People who like cold drinks (27 people)
- B: People who like hot drinks (42 people)
To find the number of people who like both coffee and tea, we can find the size of the intersection of sets A and B (A ∩ B). In other words, we need to find the number of people who belong to both sets.
By subtracting the number of people who like either cold or hot drinks (69) from the total group size (60), we can find the number of people who like both drinks:
60 - 69 = -9
It seems like we made a mistake somewhere. Since we cannot have a negative number of people, it is clear that our previous calculations were incorrect.
Given the information provided, it is not possible to determine the number of people who like both drinks. Therefore, it is not possible to calculate the probability that a person chosen at random likes both coffee and tea.