Mathematics: Astudent randomly guesses on 10 true/false questions. use the binomial model to determine the probability that the student gets 5 out of 10 questions right. show all your steps.

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Astudent randomly guesses on 10 true/false questions.

Ответ:

pinkapple2396

10.03.2022

Mathematics

0.2461

Step-by-step explanation:

The binomial distribution model formula is

$P(x)=[\frac{n!}{x!(n-x)!}]p^{x}q^{n-x}$

Where

P(x) is the probabilityn is the is total number of questions (here n = 10)x is the the number of questions we are looking for (we are looking for 5 out of 10 to be right, so x = 5)p is the probability of success (here we want 5 questions right, so probability of being right in true of false question is $\frac{1}{2}$ )q is the probability of failure (here it means getting the answer wrong, so probability of wrong is $\frac{1}{2}$ )

Now, we plug-in all the info into the formula and figure out the "probability that the student gets 5 out of 10 questions right":

$P(x)=[\frac{n!}{x!(n-x)!}]p^{x}q^{n-x}\\P(x)=[\frac{10!}{5!(10-5)!}](\frac{1}{2})^{5}(\frac{1}{2})^{10-5}\\P(x)=[\frac{10!}{5!5!}](\frac{1}{2})^{5}(\frac{1}{2})^{5}\\P(x)=[252](\frac{1}{2})^{10}\\P(x)=0.2461$

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Astudent randomly guesses on 10 true/false questions. use the binomial model to determine the probability that the student gets 5 out of 10 questions right. show all your steps.

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