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Sagot :
Answer:
a. 0.36 = 36% probability that a movie is either a comedy or produced by Warner Bros.
b. 0.2308 = 23.08% probability that a Warner Bros movie is a comedy
c. 0.1154 = 11.54% probability that a comedy has Warner Bros as its producer
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. What is the probability that a movie is either a comedy or produced by Warner Bros?
We solve this question treating these events as Venn sets.
I am going to say that:
Set A: Movie is a comedy.
Set B: Movie is produced by Warner Bros.
26% of movies coming out of Hollywood are comedies
This means that[tex]P(A) = 0.26[/tex]
Warner Bros has been the lead studio for about 13% of recent movies
This means that [tex]P(B) = 0.13[/tex]
3% of recent movies are comedies from Warner Bros.
This means that [tex]P(A \cap B) = 0.03[/tex]
The desired probability is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.26 + 0.13 - 0.03 = 0.36[/tex]
0.36 = 36% probability that a movie is either a comedy or produced by Warner Bros.
b. What is the probability that a Warner Bros movie is a comedy?
Conditional probability, in which
Event A: Produced by Warner Bros
Event B: Comedy
Warner Bros has been the lead studio for about 13% of recent movies
This means that [tex]P(A) = 0.13[/tex]
3% of recent movies are comedies from Warner Bros.
This means that [tex]P(A \cap B) = 0.03[/tex]
The desired probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.03}{0.13} = 0.2308[/tex]
0.2308 = 23.08% probability that a Warner Bros movie is a comedy.
c. What is the probability that a comedy has Warner Bros as its producer?
Now,
Event A: Comedy
Event B: Warner Bros as its producer.
About 26% of movies coming out of Hollywood are comedies
This means that [tex]P(A) = 0.26[/tex]
3% of recent movies are comedies from Warner Bros.
This means that [tex]P(A \cap B) = 0.03[/tex]
The desired probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.03}{0.26} = 0.1154[/tex]
0.1154 = 11.54% probability that a comedy has Warner Bros as its producer
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