SOLUTION: A bag contains six green marbles and nine black marbles. A marble is selected and returned to the bag. This process continues until a marble has been drawn 5 times. What is the p

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Question 1183309: A bag contains six green marbles and nine black marbles. A marble is selected and
returned to the bag. This process continues until a marble has been drawn 5 times.
What is the probability that
a) Four marbles are green?
b) Three marbles are black?

Answer by ikleyn(52893) About Me  (Show Source):
You can put this solution on YOUR website!
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A bag contains six green marbles and nine black marbles. A marble is selected and
returned to the bag. This process continues until a marble has been drawn 5 times.
What is the probability that
a) Four marbles are green?
b) Three marbles are black?
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In all, there are 6+9 = 15 marbles.

The probability to select a green marble is  6%2F15 = 2%2F5 = 0.4  at each single trial.

The probability to select a black marble is  9%2F15 = 3%2F5 = 0.6 at each single trial.


The problem is about a binomial distribution.


In case (a), the answer is  P = C%5B5%5D%5E4%2A0.4%5E4%2A0.6%5E1 = 5%2A0.4%5E4%2A0.6 = 0.0768.


In case (b), the answer is  P = C%5B5%5D%5E3%2A0.6%5E3%2A0.4%5E2 = 10%2A0.6%5E3%2A0.4%5E2 = 0.3456.

Solved.

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To see many other similar  (and different)  solved problems,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
in this site.