Weary of the low turnout in student elections, a college administration decides

Question

Weary of the low turnout in student elections, a college administration decides to choose an SRS of three students to form an advisory board that represents student opinion. Suppose that 44% of all students oppose the use of student ees to und student interest groups and that the opinions of the three students on the board are independent. Then the probability is 0.44 that each opposes the funding of interest groups. (a) Call the three students A, B, and C. Give the probability of each possible outcomes (AC, Bc, Cc are the events that the students support the student fee usage) Pr(ABC) Pr(ABCC) Pr(ABCC) Pr(A BC) Pr(ABCC) Pr(A BCS) Pr(ACBCC) (b) Let the random variable X be the number of student representatives who oppose the funding of interest groups. Give the probability distribution of X 0 2 P(x) (c) Find P (a majority of the advisory board opposes funding).

Explanation / Answer

a)P(ABC) =0.44*0.44*0.44=0.0852

P(ABCc) =0.44*0.44*(1-0.44)=0.1084

P(ABcC)=0.44*(1-0.44)*0.44 =0.1084

P(AcBC)=(1-0.44)*0.44*0.44=0.1084

P(ABcCc)=0.44*(1-0.44)*(1-0.44)=0.1380

P(AcBCc) =(1-0.44)*0.44*(1-0.44)=0.1380

P(AcBcC)=(1-0.44)*(1-0.44)*0.44 =0.1380

P(AcBcCc)=(1-0.44)*(1-0.44)*(1-0.44) =0.1756

b) from above :

c) P( a majority of advisory board opposes funding)=P(X=2)+P(X=3) =0.4104

x 0 1 2 3 P(x) 0.1756 0.4140 0.3252 0.0852

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.