Please answer

Mathematics

1 answer:

Bond [772]3 years ago

7 0

The answer is 10 years because simple interest is 16%

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A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 20 times, and the man is asked to predict

dlinn [17]

Answer:

$P(x\geq 17)=0.00128$

Step-by-step explanation:

The probability that the man gets x out of 20 correct follows a Binomial distribution, so the probability is calculated as:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}$

Where n is the number of identical experiments and p is the probability of success. In this case n is 20.

Additionally, if he has no ESP the probability that he predict correctly is 0.5, because he is only guessing.

Then, the probability that he gets x out of 20 correct is equal to:

$P(x)=\frac{20!}{x!(20-x)!}*0.5^{x}*(1-0.5)^{20-x}$

Therefore the probability that he would have done at least 17 out of 20 well if he had no ESP is:

$P(x\geq 17)=P(17)+P(18)+P(19)+P(20)\\$

Where:

$P(17)=\frac{20!}{17!(20-17)!}*0.5^{17}*(1-0.5)^{20-17}=0.00108719\\P(18)=\frac{20!}{18!(20-18)!}*0.5^{18}*(1-0.5)^{20-18}=0.00018119\\P(19)=\frac{20!}{19!(20-19)!}*0.5^{19}*(1-0.5)^{20-19}=0.00001907\\P(20)=\frac{20!}{20!(20-20)!}*0.5^{20}*(1-0.5)^{20-20}=0.00000095$