Final answer:
The probability that the Nuggets will win their next four games is found by multiplying the probability of winning one game (65% or 0.65) four times, which will result in a probability of 17.85%.
Step-by-step explanation:
The question relates to the concept of independent events in probability. When we have independent events, such as the outcomes of the basketball games in this scenario, the probability of multiple events occurring in sequence is computed by multiplying the probabilities of each individual event. Given that the probability of the Nuggets winning a basketball game is 65% or 0.65, we need to calculate the probability of them winning four games in a row.
To find this probability, we multiply the probability of winning one game four times since each game is an independent event:
- P(Win Game 1) = 0.65
- P(Win Game 2) = 0.65
- P(Win Game 3) = 0.65
- P(Win Game 4) = 0.65
We then multiply these probabilities together:
P(Win 4 Games in a Row) = P(Win Game 1) × P(Win Game 2) × P(Win Game 3) × P(Win Game 4)
= 0.65 × 0.65 × 0.65 × 0.65
= 0.1785
Therefore, the probability that the Nuggets will win their next four games is 17.85%.