Answer:
0.12 = 12% probability that a randomly selected person likes both juices.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
We solve this question treating these events as Venn probabilities.
I am going to say that.
Event A: Like orange juice.
Event B: Like grape juice.
In a survey 125 people, 90 people liked orange juice or grape juice.
This means that:
[tex]P(A \cup B) = \frac{90}{125}[/tex]
62 people who like orange juice and 43 people who like grape juice.
This means that:
[tex]P(A) = \frac{62}{125}, P(B) = \frac{43}{125}[/tex]
What is the probability that a randomly selected person likes both juices?
This is [tex]P(A \cap B)[/tex], which is given by:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex].
With the values in this problem:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = \frac{62}{125} + \frac{43}{125} - \frac{90}{125} = \frac{62 + 43 - 90}{125} = \frac{15}{125} = 0.12[/tex]
0.12 = 12% probability that a randomly selected person likes both juices.
