Mathematics: How can a baseball team win a game without a single man crossing home plate

How can a baseball team win a game without a single

Ответ:

biba54

20.11.2020

0.007773% probability that he would have done at least this well if he had no ESP.

Step-by-step explanation:

For each coin flip, there are only two possible outcomes. Either the man gets the answer right, or he does not. The probabilities for each coin toss are independent, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

He gets 22 out of 25 correct. What is the probability that he would have done at least this well if he had no ESP?

If he had no ESP, the probability of getting each flip right is p = 0.5 , since tails and heads are equally as likely.

There are 25 throws, so n = 25

This probability is

$P(X \geq 22) = P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)$

In which

$P(X = 22) = C_{25,22}.(0.50)^{22}.(0.5)^{3} = 0.000068$

$P(X = 23) = C_{25,23}.(0.50)^{23}.(0.5)^{2} = 0.000009$

$P(X = 24) = C_{25,24}.(0.50)^{24}.(0.5)^{1} = 0.0000007$

$P(X = 25) = C_{25,25}.(0.50)^{25}.(0.5)^{0} = 0.00000003$

$P(X \geq 22) = P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25) = 0.000068 + 0.000009 + 0.0000007 + 0.00000003 = 0.00007773$

0.007773% probability that he would have done at least this well if he had no ESP.

0,0(0 оценок)

How can a baseball team win a game without a single man crossing home plate

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question