Probability
p=66×100/1818=3.6303630363%
After rounding to 4 decimals:
p=3.6304%
Answer:
0.0708 = 7.08% probability that he will get exactly 6 questions right.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he guesses the wrong answer. The probability of guessing the correct answer in a question is independent from other questions. So 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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
18 questions
This means that [tex]n = 18[/tex]
True or false, guessed.
Each question has two possible answers, so [tex]p = \frac{1}{2} = 0.5[/tex]
If the student guesses, what is the probability that he will get exactly 6 questions right?
This is [tex]P(X = 6)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{18,6}.(0.5)^{6}.(0.5)^{12} = 0.0708[/tex]
0.0708 = 7.08% probability that he will get exactly 6 questions right.
