Mathematics: 2) A basketball player scores 70% of his shots on average. What is the probability that he scores at least 18 successful shots tonight if he gets 20 shots?

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2) A basketball player scores 70% of his shots

Ответ:

jorell

30.01.2022

Mathematics

3.54%

Step-by-step explanation:

This question represents a binomial distribution. A binomial distribution is given by:

$P(x)=\frac{n!}{(n-x)!x!} p^xq^{n-x}$

Where n is the total number of trials, p is the probability of success, q is the probability of failure and x is the number of success.

Given that:

A basketball player scores 70% of his shots on average, therefore p = 70% = 0.7. Also q = 1 - p = 1 - 0.7 = 0.3.

The total number of trials (n) = 20 shots

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20)

P(x = 18) = $\frac{20!}{(20-18)!18!}*0.7^{18}*0.3^{20-18}=0.0278$

P(x = 19) = $\frac{20!}{(20-19)!19!}*0.7^{19}*0.3^{20-19}=0.0068$

P(x = 20) = $\frac{20!}{(20-20)!20!}*0.7^{20}*0.3^{20-20}=0.0008$

The probability that he scores at least 18 successful shots tonight if he gets 20 shots = P(x = 18) + P(x = 19) + P(x = 20) = 0.0278 + 0.0068 + 0.0008 = 0.0354 = 3.54%

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2) A basketball player scores 70% of his shots on average. What is the probability that he scores at least 18 successful shots tonight if he gets 20 shots?

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