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A bag contains 6 red markers, 5 blue markers, and 4 green markers. A marker is randomly selected, its color is recorded, and it is returned to the bag. This is repeated 1050 times.

How many times is it expected that a red marker will be selected?

A.) approximately 280 times

B.) approximately 350 times

C.) approximately 420 times

D.) approximately 630 times

Sagot :

hpaige644

Answer:

If I am correct, the answer should be C

Step-by-step explanation:

The expected value of the red marker will be selected is 420. Then the correct option is C.

How to find that a given condition can be modeled by binomial distribution?

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

 

[tex]\rm X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]\rm P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

The expected value of X is:

[tex]\rm E(X) = np\\[/tex]

A bag contains 6 red markers, 5 blue markers, and 4 green markers.

A marker is randomly selected, its color is recorded, and it is returned to the bag.

This is repeated 1050 times.

n = 1050

Then the value of p will be

[tex]p=\dfrac{^6C_1}{^{15}C_1} = \dfrac{6}{15} = 0.4[/tex]

Then the expected value will be

[tex]\rm E(X) = np\\\\\rm E(X) = 1050 \times 0.4 \\\\\rm E(X) = 420[/tex]

Learn more about binomial distribution here:

https://brainly.com/question/13609688

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