Respuesta :
Answer:
The expected number of marbles that can be selected is [tex]\frac{200\cdot k_{Bk}}{n}[/tex].
Step-by-step explanation:
Let us consider that a bag consists different color marbles such as, blue, orange, pink, black, yellow, and so on.
The set of all the marbles can be defined as follows:
[tex]K=\{k_{Bu},\ k_{O},\ k_{P},\ k_{Bk},\ k_{Y},...\}[/tex]
Consider that the bag consists of a total of n marbles.
Suppose an event X can be defined as the selection of black marbles.
The number of black marbles in the bag is, [tex]k_{Bk}[/tex].
Compute the probability of the event X as follows:
[tex]P(X)=\frac{k_{Bk}}{n}[/tex]
A marble is selected from the bag N = 200 times, i.e. the experiment of the selection of a marble is repeated 200 times.
Every selection is independent of the other.
The success of this experiment is defined as: selecting a black marble.
The event X thus follows a Binomial experiment and the random variable X follows a Binomial distribution.
The expected value of the a Binomial random variable is:
[tex]E(X)=N\times P(X)[/tex]
Compute the expected value of X as follows:
[tex]E(X)=N\times P(X)[/tex]
[tex]=200\times \frac{k_{Bk}}{n}\\\\=\frac{200\cdot k_{Bk}}{n}[/tex]
Thus, the expected number of marbles that can be selected is [tex]\frac{200\cdot k_{Bk}}{n}[/tex].
