- \[0.005^5 \cdot (1 - 0.005)^{100 - 5}\]
The \((1 - 0.005)^{100-5}\) needs to show up since we also need to consider what the remaining \(95\) computers have done.
- \[{100 \choose 5}\]
Question 2. is interested in any \(5\) computers failing to install. It doesn’t matter which of the \(100\) fail. So this is a combination, and this combination is counted with the choose operation.
- \[{100 \choose 5}0.005^5 \cdot (1 - 0.005)^{100 - 5}\]
This is just the Binomial(\(n=100\), \(p=0.005\)) density function evaluated at \(5\).