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

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

Answer 2

0.2461

Explanation:

The binomial distribution model formula is

`P(x)=[(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
  `(1)/(2)`)
• q is the probability of failure (here it means getting the answer wrong, so probability of wrong is
  `(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)=[(n!)/(x!(n-x)!)]p^(x)q^(n-x)\\P(x)=[(10!)/(5!(10-5)!)]((1)/(2))^(5)((1)/(2))^(10-5)\\P(x)=[(10!)/(5!5!)]((1)/(2))^(5)((1)/(2))^(5)\\P(x)=[252]((1)/(2))^(10)\\P(x)=0.2461`