Answer:
0.35 = 35% probability that a married couple watches the movie
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.
The probability that a husband watches the movie, given that his wife does, is 0.7.
This means that [tex]P(B|A) = 0.7[/tex]
The probability that a wife watches the movie is 0.5.
This means that [tex]P(A) = 0.5[/tex]
What is the probability that a married couple watches the movie?
Both, so:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)*P(A) = 0.7*0.5 = 0.35[/tex]
0.35 = 35% probability that a married couple watches the movie
