The problem asks to find the probability that a basketball player, who makes 20% of shots, will make at least one shot in 14 attempts.

Steps to solve:

1. The probability of making a shot is given as $p = 0.2$.
2. The probability of missing a shot (not making a shot) is $1 - p = 0.8$.
3. The probability of missing all 14 shots (since the shots are independent) is $0.8^{14}$.
4. The probability of making at least one shot is the complement of missing all 14 shots: $P(\text{at least one shot}) = 1 - P(\text{miss all 14 shots}) = 1 - 0.8^{14}$

Let me calculate that for you.The probability that the basketball player makes at least one shot in 14 attempts is approximately $0.9560$ (rounded to 4 decimal places).

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What is the probability of missing exactly 10 out of 14 shots?
2. How would the probability change if the player attempted 20 shots instead of 14?
3. Can you calculate the expected number of successful shots in 14 attempts?
4. What if the player’s shooting accuracy improves to 30%, how does the probability change?
5. How would you calculate the probability of making exactly 5 shots out of 14 attempts?

Tip: In probability, the complement rule is often very useful for simplifying the calculation of "at least one" outcomes.