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A bag contains 30 marbles, 3 of which are blue, 20 are red, 5 are green, and 2 are purple. Emerson takes a marble out of the bag, records the color, and returns it to the bag. How many purple marbles should he expect after 300 trials?

Respuesta :

Kewlguy45
that is a pretty hard one, but about 20. 2 x 10 since there are 30 marbles, so it makes sense to say 30 x 10 to get 300, but since you only have 2 purple, you only get 2 purple out of every 30, 

SO in conclusion, 20 purple marbles.

Using the binomial distribution, it is found that he should expect 20 purple marbles should he expect after 300 trials.

The marbles are placed back into the bag, hence the trials are independent, and the binomial distribution is used.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

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

In this problem:

  • There are 300 trials, hence n = 300.
  • In each trial, 2 out of 30 marbles are purple, hence [tex]p = \frac{2}{30} = \frac{1}{15}[/tex]

Then, the expected value is of:

[tex]E(X) = np = 300\frac{1}{15} = 20[/tex]

He should expect 20 purple marbles should he expect after 300 trials.

You can learn more about the binomial distribution at https://brainly.com/question/14424710

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