The Smith's household, consisting of 3 people, used 349, 9 kWh of electricity on the post-paid system. How much would they be expected to pay (excluding VAT) for their electricity consumption?

$$\text{Remaining consumption} = 349.9 \text{ kWh} - 50 \text{ kWh} = 299.9 \text{ kWh}$$

This remaining consumption falls within the second tier (50.1 - 350 kWh), which is charged at R0.81 per kWh.

$$\text{Total Cost} = \text{R}34.50 + \text{R}242.919 = \text{R}277.419$$

Rounding to two decimal places:

$$\text{Total Cost} = \text{R}277.42$$

The Smith's household would be expected to pay (excluding VAT) $\boxed{\text{R}277.42}$.

1.1.2

Mrs Smith assumes her bill will be two-thirds of the amount calculated in QUESTION 1.1.1. We need to verify if this assumption is correct.

$$\text{Assumed New Bill} = \frac{2}{3} \times \text{R}277.419 = \text{R}184.946$$

Rounding to two decimal places:

$$\text{Assumed New Bill} = \text{R}184.95$$

Cost for the first 50 kWh:

$$\text{Cost}_{0-50} = 50 \text{ kWh} \times \text{R}0.69/\text{kWh} = \text{R}34.50$$

Remaining consumption:

$$\text{Remaining Consumption} = \frac{699.8}{3} \text{ kWh} - 50 \text{ kWh} = \frac{699.8 - 150}{3} \text{ kWh} = \frac{549.8}{3} \text{ kWh} \approx 183.267 \text{ kWh}$$

This remaining consumption falls within the second tier (50.1 - 350 kWh), charged at R0.81 per kWh.
Cost for the remaining consumption:

$$\text{Cost}_{50.1-233.267} = \frac{549.8}{3} \text{ kWh} \times \text{R}0.81/\text{kWh} = \text{R}148.446$$

$$\text{Actual New Cost} = \text{R}34.50 + \text{R}148.446 = \text{R}182.946$$

Rounding to two decimal places:

$$\text{Actual New Cost} = \text{R}182.95$$

Mrs Smith's assumed new bill: R184.95
Actual new bill: R182.95
Since $\text{R}184.95 \neq \text{R}182.95$, Mrs Smith's assumption is incorrect.

Mrs Smith's assumption is $\boxed{\text{Incorrect}}$.