Example 1. From a large batch of transistors with a high-quality rate of $90 \%$, if 5 are taken out, what is the probability that exactly 3 of them are high-quality?
Solution: Let event A: taking out 1 transistor, which is a high-quality item, $\mathrm{P}(\mathrm{A})=0.9$. This problem is to find the probability that event A occurs 3 times in 5 independent repeated trials.
$$
\mathrm{q}=1-\mathrm{P}(\mathrm{A})=1-0.9=0.1, \mathrm{n}=5 \text {, }
$$
$\mathrm{k}=3$.
$$
\therefore \mathrm{P}_{5}(3)=\mathrm{C}_{5}^{3} \times 0.9^{3} \times 0.1^{2}=0.0729 \text {. }
$$

Example 2. Example on page 103 of the textbook. Additional questions can be asked: the probability of at most 4 accurate forecasts out of 5; the probability of all 5 forecasts being inaccurate.

Note: (1) Pay attention to the meanings of "at most," "at least," and "all inaccurate." "At least 4 accurate" includes two scenarios: exactly 4 accurate and exactly 5 accurate.
(2) For the event "at most 4 accurate," there are five scenarios. However, its complementary event is simpler, which is "5 forecasts all accurate." Therefore, its probability is $1-\mathrm{P}_{5}(5)$.