Question at position 6 In a certain town, 20% of the households have an electric vehicle, 40% have a hybrid vehicle, and 10% have both. What percent of households have neither an electric nor a hybrid vehicle?0%30%10%70%50%

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Question at position 6 In a certain town, 20% of the households have an electric vehicle, 40% have a hybrid vehicle, and 10% have both. What percent of households have neither an electric nor a hybrid vehicle?0%30%10%70%50%

BlackTom AI · Accepted Answer

We’re given P(E) = 0.20, P(H) = 0.40, and P(E ∩ H) = 0.10, and we want the percent with neither electric nor hybrid.
First, recall the inclusion-exclusion principle: P(E ∪ H) = P(E) + P(H) − P(E ∩ H).
Applying the values: P(E ∪ H) = 0.20 + 0.40 − 0.10 = 0.50.
Next, the probability of neither is 1 − P(E ∪ H) = 1 − 0.50 = 0.50, or 50%.
Now evaluate each option:
- 0%: This would imply no households have either vehicle, which contradicts the given P(E) and P(H) and their overlap; it ignores the 0.20 with electric and 0.40 with hybrid. It’s inconsistent with the union probability calculated.
- 30%: If 30% had neither, then 70% would have at least one type, which would require P(E ∪ H) = 0.70. That would force P(E) + P(H) − P(E ∩ H) = 0.70, inconsistent with P(E) = 0.20, P(H) = 0.40, and P(E ∩ H) = 0.10.
- 10%: Having only 10% with neither would make P(E ∪ H) = 0.90, which is again incompatible with the given numbers; the overlap cannot compensate to reach such a high union.
- 70%: This would indicate a very large share has at least one type, implying P(E ∪ H) = 0.70 and thus P(neither) = 0.30, which contradicts the calculated 0.50 for the union.
- 50%: This matches the arithmetic from inclusion-exclusion and the complement: if 50% have at least one type, then 50% have neither. It aligns with P(E ∪ H) = 0.50 and P(neither) = 1 − 0.50 = 0.50.
In summary, the correct computation uses inclusion-exclusion to find the union, then takes the complement to obtain neither. The option that corresponds to 50% reflects this result, while the other choices conflict with the given probabilities or the fundamental relationship between union and complement.

Question at position 6 In a certain town, 20% of the households have an electric vehicle, 40% have a hybrid vehicle, and 10% have both. What percent of households have neither an electric nor a hybrid vehicle?0%30%10%70%50%

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