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. There are 4 questions following the table below. Find the probability for the first 3 questions and explain your answer for the fourth question.

The relevant equation for the Hypergeometric Distribution: P = _kC_x * _(N-k)C_(n-x)

_NC_n

k is the number "loyal" in the population

x is the number "loyal" in the sample

N is the size of the population

n is the number sampled

P is the probability of obtaining exactly x "loyal"

_kC_x is the number of combinations of k things taken x at a time or k!

(k-x)! x!

The table below is constructed using Excel to compute probabilities for obtaining exactly x "loyal" given the conditions above.