A six-sided die is rolled eleven times. What is the probability that the die will show an even number exactly nine times?
1 answer:
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You're trying to find constants 
such that 
. Equivalently, you're looking for the least-square solution to the following matrix equation.
To solve
, multiply both sides by the transpose of 
, which introduces an invertible square matrix on the LHS.
Computing this, you'd find that
which means the first choice is correct.
To solve
Computing this, you'd find that
which means the first choice is correct.