Question

HW 5.2

Answer 1

Answer:

The probability of no correct answers is 0.125 = 12.5%.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent of any other question, which means that 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.

3 trials, each with probability of success (correct) given by p=0.50.

This means that $n = 3, p = 0.5$

The probability of no correct answers is

This is P(X = 0).

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

$P(X = 0) = C_{3,0}.(0.5)^{0}.(0.5)^{3} = 0.125$

The probability of no correct answers is 0.125 = 12.5%.