Question

Помоги срочно надо. для данного баскетболиста вероятность попадания мяча в кольцо равна 0,4. Определите наиболее вероятную ситуацию попадание 3 мячей при 4 бросках мяча или попадание 4 мячей при 5 бросках мяча,если броски считаются независимыми?

Answer 1

Probability of Making a Shot

To determine the most likely scenario, we need to calculate the probabilities of making a certain number of shots given the probability of making a single shot. In this case, the probability of making a shot is 0.4.

Let's calculate the probabilities for each scenario:

1. Probability of making 3 shots in 4 attempts:

To calculate this probability, we need to use the binomial probability formula. The formula is as follows:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where: - P(X=k) is the probability of getting exactly k successes - n is the number of trials (in this case, the number of attempts) - k is the number of successes (in this case, the number of shots made) - p is the probability of success (in this case, the probability of making a shot)

Using this formula, we can calculate the probability of making 3 shots in 4 attempts:

P(X=3) = C(4, 3) * 0.4^3 * (1-0.4)^(4-3)

P(X=3) = 4 * 0.064 * 0.6

P(X=3) = 0.1536

Therefore, the probability of making 3 shots in 4 attempts is approximately 0.1536.

2. Probability of making 4 shots in 5 attempts:

Using the same formula, we can calculate the probability of making 4 shots in 5 attempts:

P(X=4) = C(5, 4) * 0.4^4 * (1-0.4)^(5-4)

P(X=4) = 5 * 0.0256 * 0.6

P(X=4) = 0.0768

Therefore, the probability of making 4 shots in 5 attempts is approximately 0.0768.

Based on these calculations, we can conclude that the most likely scenario is making 3 shots in 4 attempts, as it has a higher probability compared to making 4 shots in 5 attempts.

Please let me know if you need any further assistance!