Please answer this question are you please

A student takes an exam containing 1414 multiple choice questions. The probability of choosing a correct answer by knowledgeable

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Answer:

0.0082 = 0.82% probability that he will pass

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the students guesses the correct answer, or he guesses the wrong answer. The probability of guessing the correct answer for a question is independent of 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.

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

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.

In this problem we have that:

$n = 14, p = 0.3$ .

If the student makes knowledgeable guesses, what is the probability that he will pass?

He needs to guess at least 9 answers correctly. So

$P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)$

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

$P(X = 9) = C_{14,9}.(0.3)^{9}.(0.7)^{5} = 0.0066$

$P(X = 10) = C_{14,10}.(0.3)^{10}.(0.7)^{4} = 0.0014$

$P(X = 11) = C_{14,11}.(0.3)^{11}.(0.7)^{3} = 0.0002$

$P(X = 12) = C_{14,12}.(0.3)^{12}.(0.7)^{2} = 0.000024$

$P(X = 13) = C_{14,13}.(0.3)^{13}.(0.7)^{1} = 0.000002$

$P(X = 14) = C_{14,14}.(0.3)^{14}.(0.7)^{0} \cong 0$

$P(X \geq 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) = 0.0066 + 0.0014 + 0.0002 + 0.000024 + 0.000002 = 0.0082$

0.0082 = 0.82% probability that he will pass

6 0

3 years ago

Find the value of x.

dimaraw [331]

Answer:

$2\sqrt{77}$

Step-by-step explanation:

Use the Pythagorean theorem. $a^{2} +b^{2}=c^{2}$

a and b are the two side lengths

c is the hypotenuse (value across from the right angle)

Plug in the values that you are given.

$a^{2} +4^{2} =18^{2}$

Solve for x

$x^{2} =18^{2} -4^{2}$

$x^{2} =308$

x= $\sqrt{308}$

$x=2\sqrt{77}$

5 0

3 years ago

3. Franklin has 5 red marbles, 16 black marbles, 3 miniature green balls, and 9 miniature yellow balls in a jar at home. What is

Korolek [52]

Answer:

12:16

Step-by-step explanation:

Add the miniature balls.

3 + 9 = 12

There are 16 black marbles in the jar.

Therefore, the ratio of miniature balls to the number of black marbles is 12:16.

8 0

3 years ago

Need help asap!!!!!!

Ostrovityanka [42]

They are inverses.

The easiest way to solve this is to take the g(x) equation and switch the g(x) with the x. Then solve for your new g(x). Since it looks just like f(x) after doing that, it is an inverse.

5 0

3 years ago

Hector gave of his money and an additional $1 to Calista. He

trapecia [35]

I think it’s $34 but i’m not sure

6 0

3 years ago

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