Question 1203053
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A baseball player has a probability of 0.2 hitting the ball each time at bat, 
with successive times at bat being independent.
Calculate the probability that he gets at least 2 hits in 11 times at bat.
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<pre>
It is a typical problem on binomial distribution probability.

The number of trials is n= 11; 
the probability of success of each individual trial is p= 0.2;
the successful trials indexes are 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10 or 11.


    So,  P = P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11).


Having so many calculations to do, it is better (more economic and more efficient way) 
to transform the formula equivalently

      P = 1 - P(0) - P(1) = {{{1 - C[11]^0*0.2^0*(1-0.2)^11 - C[1]^1*0.2^1*(1-0.2)^10}}} = 

        = {{{1 - 1*1*0.8^11 - 11*0.2^1*0.8^10}}} = 0.6779  (rounded).    <U>ANSWER</U>
</pre>

Solved.