Question

In Europe, 88% of all households have a television. 51% of all households have a television and a VCR. What is the probability that a household has a VCR given that it has a television?

Answer 1

The probability that a household has a VCR given that it has a television is approximately 57.95%. This is calculated by dividing the percentage of households with both a television and VCR by the percentage of households with a television.

The probability that a household has a VCR given that it has a television can be found using the conditional probability formula:

`\[ P(\textVCR ) = \frac{P(\text{VCR and Television})}{P(\text{Television})} \]`

Given:

-
`\( P(\text{Television}) = 88\% \)` (probability that a household has a television)

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`\( P(\text{VCR and Television}) = 51\% \)` (probability that a household has both a television and a VCR)

Plug these values into the formula:

`\[ P(\text Television) = (51\%)/(88\%) \]`

`\[ P(\textVCR ) \approx (51)/(88) \]`

This simplifies to approximately:

`\[ P(\textVCR ) \approx 0.5795 \]`

Therefore, the probability that a household has a VCR given that it has a television is approximately 0.5795 or 57.95%.