Question
An animation studio works with movie theaters to learn more about the people who see its new movie. It finds that the probability that a moviegoer sees its movie on any given day is 0.14. The probability that a moviegoer is an adult is 0.64. The studio also discovers that these two events are independent.
What is the probability that a moviegoer who is an adult sees the animation studio's latest movie on any given day?
Write your answer as a decimal rounded to the nearest hundredth.
What is the probability that a moviegoer who is an adult sees the animation studio's latest movie on any given day?
Write your answer as a decimal rounded to the nearest hundredth.
Answers
GPT-4o mini
To find the probability that a moviegoer who is an adult sees the animation studio's latest movie on any given day, we can use the concept of independent events.
Let:
- \( P(S) \) = Probability that a moviegoer sees the movie = 0.14
- \( P(A) \) = Probability that a moviegoer is an adult = 0.64
Since the two events are independent, we can find the conditional probability \( P(S | A) \) (the probability that a moviegoer sees the movie given that they are an adult) as follows:
\[
P(S | A) = P(S)
\]
Thus, the probability that a moviegoer who is an adult sees the movie is still \( 0.14 \).
So, rounding this to the nearest hundredth gives:
\[
\text{Probability} = 0.14
\]
Therefore, the answer is \( \boxed{0.14} \).
Let:
- \( P(S) \) = Probability that a moviegoer sees the movie = 0.14
- \( P(A) \) = Probability that a moviegoer is an adult = 0.64
Since the two events are independent, we can find the conditional probability \( P(S | A) \) (the probability that a moviegoer sees the movie given that they are an adult) as follows:
\[
P(S | A) = P(S)
\]
Thus, the probability that a moviegoer who is an adult sees the movie is still \( 0.14 \).
So, rounding this to the nearest hundredth gives:
\[
\text{Probability} = 0.14
\]
Therefore, the answer is \( \boxed{0.14} \).