SOLUTION: There are 4 white and 7 black marbles in a basket. We are picking out them one by one and return them back to the basket. What is the chance that after picking out the marbles 7 ti

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Question 1195018: There are 4 white and 7 black marbles in a basket. We are picking out them one by one and return them back to the basket. What is the chance that after picking out the marbles 7 times, 5 of those marbles are going to be white? What is the most probable amount of white marbles being picked?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
There are 4 white and 7 black marbles in a basket.
We are picking out them one by one and return them back to the basket.
(a) What is the chance that after picking out the marbles 7 times,
5 of those marbles are going to be white?
(b) What is the most probable amount of white marbles being picked?
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Notice that in this experiment the conditions are repeating (are the same) 
for all and for each of 7 picking.


So, it is a binomial distribution experiment with 7 trials, 5 of which are 
successful and the probability of success is 4/(4+7) = 4/11 (getting white
marble) in each individual trial.


So apply the formula of probability for binomial distribution 

    P(n=7; k=5; p=4/11) = C%5B11%5D%5E4%2A%284%2F11%29%5E4%2A%281-4%2F11%29%5E%2811-4%29 = 

                        = %28%2811%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%29%29%2A%284%2F11%29%5E4%2A%287%2F11%29%5E7 = 0.243849  (rounded).    ANSWER