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
