Question

The board of directors for a particular company consists of 10 members, 6 of whom are loyal to the current company president and 4 of whom want to fire the president. Suppose the chair of the board (who is a loyal supporter of the current president) suggests to randomly select 4 other board members to serve on a committee to decide the president’s fate. Find the probability for the first 3 questions and explain your answer for the fourth question. (75–150 words, or 1–2 paragraphs) What is the probability that all 5 committee members will vote to keep the president in place, if no one changes their minds? What is the probability that a majority of the committee will vote to keep the president in place, if no one changes their minds? What is the probability that the vote is 4 to 1 to replace the president, if no one changes their minds? Imagine that you were the president of the company and you hoped to keep your position. Considering the various probabilities, would you consider the chair of the board’s suggestion to be in your favor or not? If the choice was yours, would you allow the suggestion to proceed?

Answer 1

Probability of president supporter selection = 0.6

Probability of anti-president supporter selection = 0.4

1. All the 5 members vote for president to keep,

Or Probability of selecting all the 5 members are president supporters,

P_1 = 0.6^5= 0.07776

2. Majority of members vote for president to keep,

Or Probability of selecting 3 or more from presidents side,

P_2 = (0.6^3) +(0.6^4) +(0.6^5) = 0.42336

3. Probability of 4 to 1 to replace president,

P_3 = (0.4^4)*0.6 = 0.01536

Out of there cases 2 ND case is more likely to happen and it's outcome is always continuing president. So, president can accept the deal.

But, always including all 10 members assures 100% continuity for president.