Question

A student 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.

Answer 1

Answer:

P = (10 over 5)·(1/2)^10 = 10·9·8·7·6/(5·4·3·2·1)·(1/2)^10 = 63/256

Answer 2

Answer:

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 probability
• n 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":

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