SOLUTION: 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
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Question 1026649: 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? Answer by ikleyn(52787) (Show Source):
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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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For your covenience, I am repeating this solution (its core) here again:
The probability to have 4 votes "Yes" is ;
The probability to have 5 votes "Yes" is ;
The probability to have 6 votes "Yes" is ;
The probability to have 7 votes "Yes" is .
Here the coefficients are the binomial coefficients, also known as the number of combinations of n things taken k at a time: = .
Now calculate the sum of these four particular probabilities. It is
+ + + = = 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.
