PLEASE HELP the question is in the picture above ^^
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Answer:
The expected number of marbles that can be selected is .
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:
Consider that the bag consists of a total of <em>n</em> marbles.
Suppose an event <em>X</em> can be defined as the selection of black marbles.
The number of black marbles in the bag is, .
Compute the probability of the event <em>X</em> as follows:
A marble is selected from the bag <em>N</em> = 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 <em>X</em> thus follows a Binomial experiment and the random variable <em>X</em> follows a Binomial distribution.
The expected value of the a Binomial random variable is:
Compute the expected value of <em>X</em> as follows:
Thus, the expected number of marbles that can be selected is .