To solve the problems given in the image, let's go through each part step by step.

### Part (a)
The expression is:
\[
\left(1 - \frac{1}{2}\right) \times \left(1 - \frac{1}{3}\right) \times \left(1 - \frac{1}{4}\right) \times \left(1 - \frac{1}{5}\right)
\]

Calculating each term:
- \(1 - \frac{1}{2} = \frac{1}{2}\)
- \(1 - \frac{1}{3} = \frac{2}{3}\)
- \(1 - \frac{1}{4} = \frac{3}{4}\)
- \(1 - \frac{1}{5} = \frac{4}{5}\)

Now, multiply these results together:
\[
\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5}
\]

Calculating step by step:
\[
= \frac{1 \times 2 \times 3 \times 4}{2 \times 3 \times 4 \times 5} = \frac{24}{120} = \frac{1}{5}
\]

### Part (b)
The expression is:
\[
\left(1 - \frac{3}{4}\right) \times \left(1 - \frac{3}{7}\right) \times \left(1 - \frac{3}{10}\right) \times \ldots \times \left(1 - \frac{3}{100}\right)
\]

Each term can be rewritten as:
\[
1 - \frac{3}{n} = \frac{n - 3}{n}
\]

So, we need to calculate:
\[
\frac{1 - 3/4}{4} \times \frac{1 - 3/7}{7} \times \frac{1 - 3/10}{10} \times \ldots
\]

This can be expressed as:
\[
\prod_{k=4, 7, 10, \ldots, 100} \frac{n - 3}{n}
\]

The value of \( n \) will have different values based on the specific terms included (4, 7, 10, ..., up to 100). This sequence includes \( 4, 7, 10, 13, \ldots, 100 \), which forms an arithmetic sequence where \( n = 3k + 1 \) for \( k = 1, 2, \ldots \).

If you want to calculate this product, you'd need to follow through the arithmetic sequence and sum the relevant fractions.

In summary:
- Part (a): \( \frac{1}{5} \)
- Part (b): Requires more detailed calculation based on the full list of terms.