3. Suppose any of a CEO\'s 11 directors has a chance of knowing whether the comp

Question

3. Suppose any of a CEO's 11 directors has a chance of knowing whether the company should make a particular strategic investment in China. Assume any directors knowledge is independent of any other. (a) If the CEO asks a group of 3 randomly selected directors, what is the chance that the group will (b) What number N is the smallest group of randomly chosen directors that will have at least a 50% c) If CEO asks al of his directors, what's the chance that they will not know the answer to the (d) Assuming the chance of knowing correct answers remains any board of directors would know the answer? I want a number, not a formula. chance of knowing the correct answer to the question? I want a number, not a formula. question? I want a number, not a formula. the CEO need to ensure the group of directors has a 95% chance of knowing the correct answer to the question?

Explanation / Answer

p= 1/11 ;q=10/11 .

a) Probabiliy = 1-P( none of 3 know the answer) = 1 - (10/11)^3 = 0.2486

b) 0.5 = 1-(10/11)^n

n = ln(0.5)/ln(10/11) = 7.25

Hence, 8 people are required

c) Probability = (10/11)^11=0.35

d) 0.95= 1- (10/11)^n

b = ln(0.05)/ln(10/11)= 31.43

Hence, 32 people are required

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