florvlclark
Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

In a survey 125 people, 90 people liked orange juice or grape juice. There are 62 people who like orange juice and 43 people who like grape juice. What is the probability that a randomly selected person likes both juices?

Sagot :

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.

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.