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The probability of picking a blue marble is 2/10
A bag has 5 yellow marbles, 3 red marbles, and 2 blue marbles. Quinn randomly picks a marble from the bag and returns it before another is picked. How many times would Quinn expect to pick a blue marble if he picks a marble 200 times?

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musiclover10045
the probability of picking blue is stated as 2/10 which can be reduced to 1/5
 
 multiply the number of times they pick a marble ( shown as 200) by the probability of picking a blue one ( 1/5)

200 x 1/5 = 200 / 5 = 40

Quinn can expect to pick blue 40 times

Using the binomial distribution, it is found that he should expect to pick a blue marble 40 times.

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For each trial, there are only two possible outcomes. Either a blue marble is picked, or it is not. The marble picked is returned to the box, which means that trials are independent, that is, in each trial, the probability of picking a blue marble is the same. Thus, the binomial distribution is used to solve this question.

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Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.  

The expected value is:

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

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  • 2/10 probability of picking a blue marble, thus [tex]p = \frac{2}{10} = 0.2[/tex]
  • Picks a marble 200 times, thus, [tex]n = 200[/tex]

The expected value for the number of blue marbles is:

[tex]E(X) = np = 200(0.2) = 40[/tex]

He should expect to pick a blue marble 40 times.

A similar problem is given at https://brainly.com/question/22786079

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