contestada

You randomly guess the answers to two questions on a multiple-choice test. Each question has three choices: A, B, and C.

a. What is the probability that you guess the correct answers to both questions?
$The probability is


​.
Question 2
Write the probability as a percent. Round your answer to the nearest tenth.
The probability is about
%.

Respuesta :

jbmow
1.  P=1/3 to select the correct answer from each of the two problems.  Then 1/3 x 1/3 = 1/9 to select both answers correctly.

P=11.1%

Using the binomial distribution, we have that:

1) The probability is 0.1111.

2) The probability is about 11.1%.

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

Binomial probability distribution

It is the probability of x successes on n trials, with p probability.

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

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

In this problem:

  • 2 questions, thus [tex]n = 2[/tex]
  • Each with 3 options, thus [tex]p = \frac{1}{3} = 0.3333[/tex].

Item 1:

The probability is P(X = 2), thus:

[tex]P(X = 2) = C_{2,2}.(0.3333)^{2}.(0.6667)^{0} = 0.1111[/tex]  

The probability is 0.1111.

Item 2:

As a percent, we multiply by 100%, thus:

0.111 x 100% = 11.1%.

The probability is about 11.1%.

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

Otras preguntas