Question 1026649
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The Company A has recently signed a purchase agreement with company B to acquire 100 percent interest for $20 Million. Assume that the voting power is only limited to a few trusted shareholders, the decision require a simple majority of the 7 decision-making shareholders. If each is believed to have a 0.35 probability of voting yes on the purchase, what is the probability that will be purchased by Company A? 
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I just solved it in 
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For your covenience, I am repeating this solution (its core) here again:


<pre>
The probability to have 4 votes "Yes" is  {{{C[7]^4*0.35^4}}};

The probability to have 5 votes "Yes" is  {{{C[7]^5*0.35^5}}};

The probability to have 6 votes "Yes" is  {{{C[7]^6*0.35^6}}};

The probability to have 7 votes "Yes" is  {{{C[7]^7*0.35^7}}}.

Here the coefficients  {{{C[n]^k}}} are the binomial coefficients, also known as the number of combinations of n things taken k at a time:  {{{C[n]^k}}} = {{{n!/(k!*(n-k)!)}}}.

Now calculate the sum of these four particular probabilities. It is

  {{{C[7]^4*0.35^4}}} + {{{C[7]^5*0.35^5}}} + {{{C[7]^6*0.35^6}}} + {{{C[7]^7*0.35^7}}} = {{{35*0.35^4 + 21*0.35^5 + 7*0.35^6 + 1*0.35^7}}} = 0.649.

Thus the probability to have the majority of votes "Yes" (4 or 5 or 6 or 7 votes) is equal to 0.649.
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