Final answer:
To find the probability of getting at least 3 hits in the game, we can use the binomial probability formula. By calculating the probabilities of getting 0, 1, and 2 hits, we find that the probability of getting less than 3 hits is approximately 0.99. Therefore, the probability of getting at least 3 hits is approximately 0.01, or 1%.
Step-by-step explanation:
To find the probability that the basketball player will get at least 3 hits in the game, we can use the binomial probability formula. The formula is: P(X ≥ k) = 1 - P(X < k), where X is the number of hits, and k is the minimum number of hits we are interested in.
In this case, X follows a binomial distribution with a probability of success (getting a hit) of 0.2. We want to find P(X ≥ 3), so we need to calculate P(X < 3) and subtract it from 1.
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
Using the binomial probability formula, we can calculate each term:
P(X = 0) = (5 choose 0) * (0.2)^0 * (0.8)^5 = 1 * 1 * (0.8)^5 ≈ 0.32
P(X = 1) = (5 choose 1) * (0.2)^1 * (0.8)^4 = 5 * 0.2 * (0.8)^4 ≈ 0.41
P(X = 2) = (5 choose 2) * (0.2)^2 * (0.8)^3 = 10 * (0.2)^2 * (0.8)^3 ≈ 0.26
Therefore, P(X < 3) = 0.32 + 0.41 + 0.26 ≈ 0.99
Finally, we can calculate P(X ≥ 3) by subtracting P(X < 3) from 1:
P(X ≥ 3) = 1 - 0.99 = 0.01
So the probability that the basketball player will get at least 3 hits in the game is approximately 0.01, or 1%.