Respuesta :
Answer:
0.579 is the probability that a household has a VCR given they have a TV.
Step-by-step explanation:
We are given the following in the question:
Probability of all households have a TV = 88% = 0.88
[tex]P(T) = 0.88[/tex]
Probability of all households have a TV and VCR = 51% = 0.51
[tex]P(T\cap V) = 0.51[/tex]
We have to find the probability that a household has a VCR given they have a TV.
The conditional probability is given by:
[tex]P(V|T) = \displaystyle\frac{P(V\cap T)}{P(t)} = \frac{0.51}{0.88} = 0.579[/tex]
0.579 is the probability that a household has a VCR given they have a TV.
Using conditional probability, it is found that there is a 0.5795 = 57.95% probability that a household has a VCR given they have a TV.
Conditional Probability
[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.
In this problem:
- Event A: Household has a TV.
- Event B: Household has a VCR.
- 88% of all households have a TV, hence [tex]P(A) = 0.88[/tex].
- 51% of all households have a TV and VCR, hence [tex]P(A \cap B) = 0.51[/tex].
Hence, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.51}{0.88} = 0.5795[/tex]
0.5795 = 57.95% probability that a household has a VCR given they have a TV.
You can learn more about conditional probability at https://brainly.com/question/14398287
