In a survey of 380 households regarding the ownership of VCRs and DVD players, the following data was obtained:


350 households own one or more VCRs.
​180 households own one or more VCRs and one or more DVD players.
​13 households do not own a VCR or a DVD player.

How many households only own one or more DVD players?

20 households
29 households
19 households
16 households
17 households
30 households

Please explain. thank you

Total=VCR+DVD Only +13

380 =350 +DVD only-13
DVDonly=30-13=17

A venn diagram helps.

To find the number of households that only own one or more DVD players, we need to subtract the number of households that own both VCRs and DVD players from the total number of households that own DVD players.

First, let's find the number of households that own DVD players. We know that 13 households do not own either a VCR or a DVD player, so we subtract this from the total number of households:

Total households - Households without VCRs or DVD players = Total households with VCRs or DVD players
380 - 13 = 367 households with VCRs or DVD players

Next, we need to find the number of households that own both VCRs and DVD players. We know that 180 households own at least one VCR and one DVD player.

Total households with VCRs or DVD players - Households with both VCRs and DVD players = Households with only DVD players
367 - 180 = 187 households with only DVD players

Therefore, the answer is 187 households.

To find out how many households only own one or more DVD players, we need to subtract the number of households that own both VCRs and DVD players from the total number of households that own one or more DVD players.

From the given data, we know the following:
- 350 households own one or more VCRs.
- 180 households own one or more VCRs and one or more DVD players.
- 13 households do not own a VCR or a DVD player.

To calculate the number of households that only own one or more DVD players, we can use the principle of inclusion-exclusion.

First, we need to find the total number of households that own one or more DVD players. We do this by adding the number of households that own both VCRs and DVD players to the number of households that only own DVD players: 180 (own both) + x (only own DVD players).

We also know that the total number of households is 380 (given in the survey).

So, we can set up an equation:
350 (own VCRs) + 180 (own both) + x (only own DVD players) + 13 (own neither) = 380.

To find x (the number of households that only own DVD players), we rearrange the equation:
350 + 180 + x + 13 = 380.
x = 380 - (350 + 180 + 13).
x = 380 - 543.
x = -163.

However, a negative number of households does not make sense in this context. This discrepancy suggests that there may be an error in the given data. It's possible that the number of households that own VCRs and DVD players (180) was recorded incorrectly, resulting in an invalid calculation. Therefore, we cannot reliably determine the number of households that only own one or more DVD players based on the given data.