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Find the probability of answering the two multiple choice questions correctly if random guesses are made. assume the questions each have five choices for the answer. only one of the choices is correct.
a. 0.004
b. 0.4
c. 0.02
d. 0.04

Respuesta :

andyzhu68
Chance of guessing correctly for one problem: 1/5
Chance of guessing correctly for two problems: 1/5*1/5=1/25
To put that into decimal it would be 0.04.
The correct answer is D.

Using the binomial distribution, it is found that there is a 0.04 probability of answering the two multiple choice questions correctly, given by option D.

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For each question, there are only two possible outcomes. Either the correct guess is made, or it is not. The probability of the correct guess being made in a question is independent of any other question, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

p is the probability of a success on a single trial.

In this problem:

  • Two questions, thus [tex]n = 2[/tex].
  • One of the five options is correct, thus [tex]p = \frac{1}{5} = 0.2[/tex].
  • The probability that both are correct is P(X = 2), then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,2}.(0.2)^{2}.(0.8)^{0} = 0.04[/tex]

0.04 probability of answering the two multiple choice questions correctly if random guesses are made, option D.

A similar problem is given at https://brainly.com/question/24863377

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